uniqueness of gradient gibbs measures with disorder we consider in a uniformly strictly convex potential regime two versions of random gradient models with disorder in model a the interface feels a bulk term of random fields while in model b the disorder enters through the potential acting on the gradients we assume a general distribution on the disorder with uniformly bounded finite second moments it is well known that for gradient models without disorder there are no gibbs measures in infinite volume in dimension d 2 while there are shift invariant gradient gibbs measures describing an infinite volume distribution for the gradients of the field as was shown by funaki and spohn commun math phys 185 1 36 1997 van enter and kulske proved in ann appl probab 18 1 109 119 2008 that adding a disorder term as in model a prohibits the existence of such gradient gibbs measures for general interaction potentials in d 2 in cotar and kulske ann appl probab 22 5 1650 1692 2012 we proved the existence of shift covariant random gradient gibbs measures for model a when d ge 3 the disorder is i i d and has mean zero and for model b when d ge 1 and the disorder has a stationary distribution in the present paper we prove existence and uniqueness of shift covariant random gradient gibbs measures with a given expected tilt u in mathbb r d and with the corresponding annealed measure being ergodic for model a when d ge 3 and the disordered random fields are i i d and symmetrically distributed and for model b when d ge 1 and for any stationary disorder dependence structure we also compute for both models for any gradient gibbs measure constructed as in cotar and kulske ann appl probab 22 5 1650 1692 2012 when the disorder is i i d and its distribution satisfies a poincare inequality assumption the optimal decay of covariances with respect to the averaged over the disorder gradient gibbs measure

internal diffusion limited aggregation parallel algorithms and complexity the computational complexity of internal diffusion limited aggregation dla is examined from both a theoretical and a practical point of view we show that for two or more dimensions the problem of predicting the cluster from a given set of paths is complete for the complexity class cc the subset of p characterized by circuits composed of comparator gates cc completeness is believed to imply that in the worst case growing a cluster of size n requires polynomial time in n even on a parallel computer a parallel relaxation algorithm is presented that uses the fact that clusters are nearly spherical to guess the cluster from a given set of paths and then corrects defects in the guessed cluster through a nonlocal annihilation process the parallel running time of the relaxation algorithm for two dimensional internal dla is studied by simulating it on a serial computer the numerical results are compatible with a running time that is either polylogarithmic in n or a small power of n thus the computational resources needed to grow large clusters are significantly less on average than the worst case analysis would suggest for a parallel machine with k processors we show that random clusters in d dimensions can be generated in mathcal o n k logk n 2 d steps this is a significant speedup over explicit sequential simulation which takes mathcal o n 1 2 d time on average finally we show that in one dimension internal dla can be predicted in mathcal o logn parallel time and so is in the complexity class nc

from logarithmic to subdiffusive polynomial fluctuations for internal dla and related growth models we consider a cluster growth model on zd called internal diffusion limited aggregation internal dla in this model random walks start at the origin one at a time and stop moving when reaching a site not occupied by previous walks it is known that the asymptotic shape of the cluster is spherical when dimension is 2 or more we prove that fluctuations with respect to a sphere are at most a power of the logarithm of its radius in dimension d 2 in so doing we introduce a closely related cluster growth model that we call the flashing process whose fluctuations are controlled easily and accurately this process is coupled to internal dla to yield the desired bound part of our proof adapts the approach of lawler bramson and griffeath on another space scale and uses a sharp estimate written by blachere in our appendix on the expected time spent by a random walk inside an annulus

limiting shapes for deterministic centrally seeded growth models we study the rotor router model and two deterministic sandpile models for the rotor router model in z d levine and peres proved that the limiting shape of the growth clus ter is a sphere for the other two models only bounds in dimension 2 are known a unified approach for these models with a new parameter h the initial number of particles at each site allows to prove a number of new limiting shape results in any dimension d 1 for the rotor router model the limiting shape is a sphere for all values of h for one of the sandpile models and h 2d 2 the maximal value the limiting shape is a cube for both sandpile models the limiting shape is a sphere in the limit h finally we prove that the rotor router shape contains a diamond

robust nonparametric cyclic correlation based spectrum sensing for cognitive radio cognitive radios sense the radio spectrum in order to find underutilized spectrum and then exploit it in an agile manner spectrum sensing has to be performed reliably in challenging propagation environments characterized by shadowing and fading effects as well as heavy tailed noise distributions in this paper a robust computationally efficient nonparametric cyclic correlation estimator based on the multivariate spatial sign function is proposed nonparametric statistics provide additional robustness against heavy tailed noise and when the noise statistics are not fully known asymptotic distribution of the spatial sign cyclic correlation estimator under the null hypothesis is established tests using constraint on false alarm rate are derived based on the estimated spatial sign cyclic correlation for single user and collaborative spectrum sensing by multiple secondary users theoretical justification for detecting cyclostationary signals using the spatial sign cyclic correlation is provided a sequential detection scheme for reducing the average detection time is proposed simulation experiments and theoretical results comparing the proposed method with cyclostationary spectrum sensing methods employing the conventional cyclic correlation estimator are presented simulations demonstrate the reliable and highly robust performance of the proposed nonparametric spectrum sensing method in both gaussian and non gaussian noise environments

collaborative cyclostationary spectrum sensing for cognitive radio systems this paper proposes an energy efficient collaborative cyclostationary spectrum sensing approach for cognitive radio systems an existing statistical hypothesis test for the presence of cyclostationarity is extended to multiple cyclic frequencies and its asymptotic distributions are established collaborative test statistics are proposed for the fusion of local test statistics of the secondary users and a censoring technique in which only informative test statistics are transmitted to the fusion center fc during the collaborative detection is further proposed for improving energy efficiency in mobile applications moreover a technique for numerical approximation of the asymptotic distribution of the censored fc test statistic is proposed the proposed tests are nonparametric in the sense that no assumptions on data or noise distributions are required in addition the tests allow dichotomizing between the desired signal and interference simulation experiments are provided that show the benefits of the proposed cyclostationary approach compared to energy detection the importance of collaboration among spatially displaced secondary users for overcoming shadowing and fading effects as well as the reliable performance of the proposed algorithms even in very low signal to noise ratio snr regimes and under strict communication rate constraints for collaboration overhead

statistical tests for presence of cyclostationarity the presence of kth order cyclostationarity is defined in terms of nonvanishing cyclic cumulants or polyspectra relying upon the asymptotic normality and consistency of kth order cyclic statistics asymptotically optimal spl chi sup 2 tests are developed to detect the presence of cycles in the kth order cyclic cumulants or polyspectra without assuming any specific distribution on the data constant false alarm rate tests are derived in both time and frequency domain and yield consistent estimates of possible cycles present in the kth order cyclic statistics explicit algorithms for k spl les 4 are discussed existing approaches are rather empirical and deal only with k spl les 2 case simulation results are presented to confirm the performance of the given tests

the limiting shape for drifted internal diffusion limited aggregation is a true heat ball we build the idla cluster using drifted random walks and study the limiting shapes they exhibit with the help of sandpile models for constant drift the normalised cluster converges to a canonical shape s which can be termed a true heat ball in that it gives rise to a mean value property for caloric functions the existence and boundedness of such a shape answers the natural yet open question of the existence and boundedness of a shape that satisfies a mean value property for caloric functions

detection of multivariate cyclostationarity this paper derives an asymptotic generalized likelihood ratio test glrt and an asymptotic locally most powerful invariant test lmpit for two hypothesis testing problems 1 is a vector valued random process cyclostationary cs or is it wide sense stationary wss 2 is a vector valued random process cs or is it nonstationary our approach uses the relationship between a scalar valued cs time series and a vector valued wss time series for which the knowledge of the cycle period is required this relationship allows us to formulate the problem as a test for the covariance structure of the observations the covariance matrix of the observations has a block toeplitz structure for cs and wss processes by considering the asymptotic case where the covariance matrix becomes block circulant we are able to derive its maximum likelihood ml estimate and thus an asymptotic glrt moreover using wijsman s theorem we also obtain an asymptotic lmpit these detectors may be expressed in terms of the loeve spectrum the cyclic spectrum and the power spectral density establishing how to fuse the information in these spectra for an asymptotic glrt and lmpit this goes beyond the state of the art where it is common practice to build detectors of cyclostationarity from ad hoc functions of these spectra

asymptotic performance analysis of cyclic detectors the paper deals with the analytical evaluation of the asymptotic detection and false alarm probabilities of multicycle and single cycle detectors operating in additive white gaussian noise with unknown and nonrandom spectral level which are based on the cyclostationarity properties of the signal to be intercepted the receiver operating characteristics are derived by using the asymptotic complex normality and the covariance expression of the sample average estimator of the cyclic covariance in an observed discrete time series a numerical example for interception of a binary phase shift keying signal is considered

one dimensional long range diffusion limited aggregation i we examine diffusion limited aggregation generated by a random walk on zz with long jumps we derive upper and lower bounds on the growth rate of the aggregate as a function of the number of moments a single step of the walk has under various regularity conditions on the tail of the step distribution we prove that the diameter grows as n o 1 n o 1 with an explicitly given the growth rate of the aggregate is shown to have three phase transitions when the walk steps have finite third moment finite variance and conjecturally finite half moment

a modified pseudolikelihood approach for analysis of longitudinal data we consider the analysis of longitudinal data when the covariance function is modeled by additional parameters to the mean parameters in general inconsistent estimators of the covariance variance correlation parameters will be produced when the working correlation matrix is misspecified which may result in great loss of efficiency of the mean parameter estimators albeit the consistency is preserved we consider using different working correlation models for the variance and the mean parameters in particular we find that an independence working model should be used for estimating the variance parameters to ensure their consistency in case the correlation structure is misspecified the designated working correlation matrices should be used for estimating the mean and the correlation parameters to attain high efficiency for estimating the mean parameters simulation studies indicate that the proposed algorithm performs very well we also applied different estimation procedures to a data set from a clinical trial for illustration

autocorrelation based decentralized sequential detection of ofdm signals in cognitive radios this paper introduces a simple and computationally efficient spectrum sensing scheme for orthogonal frequency division multiplexing ofdm based primary user signal using its autocorrelation coefficient further it is shown that the log likelihood ratio test llrt statistic is the maximum likelihood estimate of the autocorrelation coefficient in the low signal to noise ratio snr regime performance of the local detector is studied for the additive white gaussian noise awgn and multipath channels using theoretical analysis obtained results are verified in simulation the performance of the local detector in the face of shadowing is studied by simulations a sequential detection sd scheme where many secondary users cooperate to detect the same primary user is proposed user cooperation provides diversity gains as well as facilitates using simpler local detectors the sequential detection reduces the delay and the amount of data needed in identification of the underutilized spectrum the decision statistics from individual detectors are combined at the fusion center fc the statistical properties of the decision statistics are established the performance of the scheme is studied through theory and validated by simulations a comparison of the sd scheme with the neyman pearson fixed sample size fss test for the same false alarm and missed detection probabilities is also carried out

on cyclostationarity based spectrum sensing under uncertain gaussian noise detection of cyclostationary primary user pu signals in colored gaussian noise for cognitive radio systems is considered based on looking for single or multiple cycle frequencies at single or multiple time lags in the cyclic autocorrelation function caf of the noisy pu signal we explicitly exploit the knowledge that under the null hypothesis of pu signal absent the measurements originate from possible colored gaussian noise with unknown correlation function our formulation allows us to simplify the spectrum sensing detector and obviates the need for estimating an unwieldy covariance matrix needed in some prior works we consider both single and multiple antenna receivers and both nonconjugate and conjugate cafs a performance analysis of the proposed detector is carried out supporting simulation examples are provided to demonstrate the efficacy of the proposed approaches and to compare them with some existing approaches our proposed approaches are computationally cheaper than the dandawate giannakis and related approaches while having quite similar detection performance for a given false alarm rate

blind stbc identification for multiple antenna ofdm systems this paper addresses the problem of space time block code stbc identification for multiple antenna ma orthogonal frequency division multiplexing ofdm systems operating over frequency selective channels for the first time in literature previous investigations published on the topic of stbc identification were restricted to single carrier systems operating over frequency flat channels ofdm systems make this topic more challenging to handle since the identifiers work in frequency selective channels with little or no knowledge of the beginning of the ofdm blocks ofdm parameters and frequency selective channel coefficients we show that by taking advantage of the space time redundancy stbc identification can be performed by exploiting the cross correlation of the signals received from different antennas as a discriminating feature using this feature we develop a binary hypothesis test for decision making the proposed method does not require information about the channel coefficients modulation format noise power or timing of the ofdm and stbc blocks moreover it does not need accurate knowledge of either clock timing information or ofdm parameters including the number of sub carriers and cyclic prefix length extensive simulation experiments have verified the effectiveness of the proposed method

high order moments and gaussianity of single carrier and ofdm signals this paper analyzes the high order moments of linearly modulated single carrier as well as orthogonal frequency division multiplexing ofdm signals assuming that the modulated symbols that form resulting continuous signal waveform are statistically independent for a single carrier case with the ideal low pass filter used for pulse shaping closed form expressions of the moments with up to the eighth order are derived the proposed approach is then extended to gaussianity assessment of ofdm signals we show how the moments of ofdm signals can approach to those of gaussian distribution as the number of subcarriers increases for a given modulation constraint on each subcarrier also reported is the peculiar nonstationary behavior of the fourth order moments in the case of bpsk modulated ofdm signals

new user identification in a cdma system we present three detector estimators des which allow multiuser detection and parameter estimation without a side channel in a dynamic asynchronous code division multiple access cdma system in which users are entering and leaving the system these des optimally detect a new user given only the chip rate and the spreading factor of the new user two of these des the maximum likelihood detector estimator mlde and the generalized maximum likelihood detector estimator gmlde produce maximum likelihood estimates of the new user s signature sequence delay and amplitude which are then incorporated into a multiuser detector the third de the cyclic detector estimator cde is the most computationally efficient of the three processors this de detects the new user by testing for cyclostationarity and then uses suboptimal schemes to estimate the new user s signature sequence delay and amplitude simulations indicate that all three des reliably detect a new user for an e sub s spl sigma sup 2 symbol energy to noise ratio of 5 db the mlde and gmlde produce signature sequence and delay estimates with probability of error less than 0 07 for an e sub s spl sigma sup 2 of 10 db and the cde produces signature sequence and delay estimates with probability of error less than 0 13 for an e sub s spl sigma sup 2 of 15 db

fluctuation results for hastings levitov planar growth we study the fluctuations of the outer domain of hastings levitov clusters in the small particle limit these are shown to be given by a continuous gaussian process mathcal f taking values in the space of holomorphic functions on z 1 of which we provide an explicit construction the boundary values mathcal w of mathcal f are shown to perform an ornstein uhlenbeck process on the space of distributions on the unit circle mathbb t which can be described as the solution to the stochastic fractional heat equation begin aligned frac partial partial t mathcal w t vartheta delta 1 2 mathcal w t vartheta sqrt 2 xi t vartheta end aligned where delta denotes the laplace operator acting on the spatial component and xi t vartheta is a space time white noise as a consequence we find that when the cluster is left to grow indefinitely the boundary process mathcal w converges to a log correlated fractional gaussian field which can be realised as delta 1 4 w for w complex white noise on mathbb t

identification of quasi periodically varying systems using the combined nonparametric parametric approach the problem of identification of quasi periodically varying finite impulse response systems is considered neither the number of system frequency modes nor the initial frequency values are assumed to be known a priori the proposed solution is a blend of the parametric model based and nonparametric discrete fourier transform based approach to system identification it is shown that the results of nonparametric analysis can be used to identify the number of frequency modes and to determine initial conditions needed to smoothly start or restart the model based tracking algorithm such a combined nonparametric parametric approach allows one to preserve advantages of both frameworks leading to an estimation procedure which guarantees global frequency search high frequency resolution fast initial convergence and good steady state tracking capabilities

cyclic statistic estimators with uncertain cycle frequencies for almost cyclostationary processes sufficient conditions are derived such that estimates of the second order cyclic probabilistic functions with estimated cycle frequencies are mean square consistent and asymptotically complex normal cyclic conjugate autocorrelation functions and cyclic conjugate spectra are considered under the derived conditions asymptotically as the data record length approaches infinity the estimates of cyclic statistics with estimated cycle frequencies have the same complex normal distribution as the case of exactly known cycle frequencies the results are applied to the detection of a moving cyclostationary source in the presence of strong doppler effect and for low values of snr

nonparametric cyclic polyspectral analysis of am signals and processes with missing observations by viewing discrete time amplitude modulated signals and processes with missing observations as cyclostationary signals nonparametric mean square sense consistent and asymptotically normal single record estimators are developed for their kth order cumulants and polyspectra along with the asymptotic covariances the proposed estimation schemes use cyclic cumulants and polyspectra and are theoretically insensitive to any additive stationary noise in addition schemes of order k or 3 convey complete phase information and are insensitive to additive cyclostationary gaussian noise of unknown covariance the conventional approaches cannot recover mixed phase linear processes are susceptible to additive noise and are a special case of the proposed schemes simulations demonstrate superior performance of the proposed algorithms

on spectral theory of cyclostationary signals in multirate systems this paper studies two problems in the spectral theory of discrete time cyclostationary signals the cyclospectrum representation and the cyclospectrum transformation by linear multirate systems four types of cyclospectra are presented and their interrelationships are explored in the literature the problem of cyclospectrum transformation by linear systems was investigated only for some specific configurations and was usually developed with inordinate complexities due to lack of a systematic approach a general multirate system that encompasses most common systems linear time invariant systems and linear periodically time varying systems is proposed as the unifying framework more importantly it also includes many configurations that have not been investigated before e g fractional sample rate changers with cyclostationary inputs the blocking technique provides a systematic solution as it associates a multirate system with an equivalent linear time invariant system and cyclostationary signals with stationary signals thus the original problem is elegantly converted into a relatively simple one which is solved in the form of matrix multiplication

identification of closed loop linear systems via cyclic spectral analysis given noisy input output time domain data the problem of closed loop system identification given noisy time domain input output measurements is considered it is assumed that the various disturbances affecting the system are zero mean stationary whereas the closed loop system operates under an external cyclostationary input which is not measured noisy measurements of the direct input and output of the plant are assumed to be available the closed loop system must be stable but it is allowed to be unstable in open loop no knowledge about the linear feedback mechanism is assumed two identification algorithms are investigated using cyclic spectral analysis of noisy input output data for both approaches the open loop transfer function is first estimated using the cyclic spectrum and cyclic cross spectrum of the input output data these transfer function estimates are then used as data for the proposed algorithms both classes of parameter estimators are shown to be weakly consistent in any stationary noise both at input as well as output asymptotic performance analysis of the proposed parameter estimators is also provided computer simulation examples are presented in support of the proposed approaches

multirate processing of time series exhibiting higher order cyclostationarity the paper investigates the effects of multirate systems on the higher order wide sense cyclostationarity wscs properties of discrete time series to this end definitions and properties of the cyclic higher order statistics which were introduced for continuous time series in the fraction of time probability framework are first extended to discrete time series then starting from the consideration of the basic multirate building blocks viz m fold decimators and l fold interpolators results for typical interconnections are derived the problem of eliminating the images in the cyclic higher order spectra of an interpolated time series is addressed moreover the problem of avoiding aliasing in both cycle and spectral frequency domains in the cyclic higher order spectra of a decimated time series is considered finally a sufficient condition to avoid both aliasing and imaging effects in the cyclic higher order spectra of a time series decimated by a fractional factor is derived

internal dla and the gaussian free field in previous works we showed that the internal diffusion limited aggregation dla cluster on zd with t particles is almost surely spherical up to a maximal error of o logt if d 2 and o logt if d 3 this paper addresses average error in a certain sense the average deviation of internal dla from its mean shape is of constant order when d 2 and of order r1 d 2 for a radius r cluster in general appropriately normalized the fluctuations taken over time and space scale to a variant of the gaussian free field

lower bounds on fluctuations for internal dla we consider internal diffusion limited aggregation in dimension two or more this is a random cluster growth model where random walks start at the origin of the lattice one at a time and stop moving when reaching a site that is not occupied by previous walks when n random walks are sent from the origin we establish a lower bound for the inner and outer errors fluctuations of order square root of the logarithm of n when dimension is three or more this lower bound matches the upper bound recently obtained in independent works of asselah and gaudilliere ann prob arxiv 1011 4592 2010 and jerison et al internal dla and the gaussian free field arxiv 1012 3453 2010 also we produce as a corollary of our proof of asselah and gaudilliere ann prob arxiv 1011 4592 2010 an upper bound for the fluctuation of the inner error in a specified direction

time domain tests for gaussianity and time reversibility statistical signal processing algorithms often rely upon gaussianity and time reversibility two important notions related to the probability structure of stationary random signals and their symmetry parametric models obtained via second order statistics sos are appropriate when the available data is gaussian and time reversible on the other hand evidence of nonlinearity non gaussianity or time irreversibility favors the use of higher order statistics hos in order to validate gaussianity and time reversibility and quantify the tradeoffs between sos and hos consistent time domain chi squared statistical tests are developed exact asymptotic distributions are derived to estimate the power of the tests including a covariance expression for fourth order sample cumulants a modification of existing linearity tests in the presence of additive gaussian noise is discussed briefly the novel gaussianity statistic is computationally attractive leads to a constant false alarm rate test and is well suited for parametric modeling because it employs the minimal hos lags which uniquely characterize arma processes simulations include comparisons with an existing frequency domain approach and an application to real seismic data time reversibility tests are also derived and their performance is analyzed both theoretically and experimentally

internal diffusion limited aggregation on discrete groups having exponential growth the internal diffusion limited aggregation dla has been introduced by diaconis and fulton rend sem mat univ pol torino 49 95 119 1991 it is a growth model defined on an infinite set and associated to a markov chain on this set we focus here on sets which are finitely generated groups with exponential growth we prove a shape theorem for the internal dla on such groups associated to symmetric random walks for that purpose we introduce a new distance associated to the green function which happens to have some interesting properties in the case of homogeneous trees we also get the right order for the fluctuations of that model around its limiting shape

threshold growth dynamics we study the asymptotic shape of the occupied region for monotone deterministic dynamics in d dimensional euclidean space parametrized by a threshold 0 and a borel set n r d with positive and finite lebesgue measure if a n denotes the oocupied set of the dynamics at integer time n then a n 1 is obtained by adjoining any point x for which the volume of overlap between x n and a n exceeds except in some degenerate cases we prove that n 1 a n converges to a unique limiting shape l starting from any bounded initial region a 0 that is suitably large moreover l is computed as the polar transform for 1 w where w is an explicit width function that depends on n and

nonparametric polyspectral estimators for kth order almost cyclostationary processes second and higher order almost cyclostationary processes are random signals with almost periodically time varying statistics the class includes stationary and cyclostationary processes as well as many real life signals of interest cyclic and time varying cumulants and polyspectra are defined for discrete time real kth order cyclostationary processes and their interrelationships are explored smoothed polyperiodograms are proposed for cyclic polyspectral estimation and are shown to be consistent and asymptotically normal asymptotic covariance expressions are derived along with their computable forms higher than second order cyclic cumulants and polyspectra convey time varying phase information and are theoretically insensitive to any stationary for nonzero cycles as well as additive cyclostationary gaussian noise for all cycles

nonparametric estimation of the cyclic cross spectrum cyclostationary processes are an important class of nonstationary processes we consider nonparametric estimation of the cyclic cross spectrum a smoothed periodogram based estimator is studied and its asymptotic behavior characterized extending univariate work to the multivariate case application to cyclic coherence measurements is discussed the results are useful in a variety of multisensor cyclostationary signal processing scenarios such as time delay and bearing estimation

performance analysis of cyclic statistics for the estimation of harmonics in multiplicative and additive noise the problem of estimating the frequencies of harmonics in multiplicative and additive noise is addressed the cyclic mean cm can be used if the multiplicative noise has nonzero mean the cyclic variance cv can be used whether or not the multiplicative noise has zero mean this paper answers the following question under what conditions should we use the cv instead of the cm the criteria used are the ease of detection and the accuracy of estimation the cv is preferable to the cm if the coherent to noncoherent harmonic power ratio is less than a threshold that depends on the first four cumulants when the noises are colored this threshold becomes frequency dependent third and fourth order cyclic statistics are also studied and it is shown that they will always be outperformed either by the cm or cv when the multiplicative noise is symmetric

logarithmic fluctuations for internal dla let each of n particles starting at the origin in z 2 perform simple random walk until reaching a site with no other particles lawler bramson and griffeath proved that the resulting random set a n of n occupied sites is with high probability close to a disk br of radius r p n we show that the discrepancy between a n and the disk is at most logarithmic in the radius i e there is an absolute constant c such that with probability 1 br c log r a r 2 br c log r for all suciently large r

pattern formation in fast growing sandpiles we study the patterns formed by adding n sand grains at a single site on an initial periodic background in the abelian sandpile models and relaxing the configuration when the heights at all sites in the initial background are low enough one gets patterns showing proportionate growth with the diameter of the pattern formed growing as n 1 d for large n in d dimensions on the other hand if sites with maximum stable height in the starting configuration form an infinite cluster we get avalanches that do not stop in this paper we describe our unexpected finding of an interesting class of backgrounds in two dimensions that show an intermediate behavior for any n the avalanches are finite but the diameter of the pattern increases as n for large n with 1 2 1 different values of can be realized on different backgrounds and the patterns still show proportionate growth the non compact nature of growth simplifies their analysis significantly we characterize the asymptotic pattern exactly for one illustrative example with 1

detection of an anomalous cluster in a network we consider the problem of detecting whether or not in a given sensor network there is a cluster of sensors which exhibit an unusual behavior formally suppose we are given a set of nodes and attach a random variable to each node we observe a realization of this process and want to decide between the following two hypotheses under the null the variables are i i d standard normal under the alternative there is a cluster of variables that are i i d normal with positive mean and unit variance while the rest are i i d standard normal we also address surveillance settings where each sensor in the network collects information over time the resulting model is similar now with a time series attached to each node we again observe the process over time and want to decide between the null where all the variables are i i d standard normal and the alternative where there is an emerging cluster of i i d normal variables with positive mean and unit variance the growth models used to represent the emerging cluster are quite general and in particular include cellular automata used in modelling epidemics in both settings we consider classes of clusters that are quite general for which we obtain a lower bound on their respective minimax detection rate and show that some form of scan statistic by far the most popular method in practice achieves that same rate within a logarithmic factor our results are not limited to the normal location model but generalize to any one parameter exponential family when the anoma lous clusters are large enough

analysis of a drop push model for percolation and coagulation in this article we study a type of a one dimensional percolation and coagulation model whose basic features include a sequential dropping of particles on a substrate followed by their transport via a pushing mechanism particles are dropped onto a one dimensional lattice and carry out a random walk until they encounter an empty site where they become stuck in such a model calculating the probability of coalescence of two arbitrary clusters of particles we embed a certain coalescence process called the additive marcus lushnikov process which converges to a particular solution of the smoluchowski equation throughout we study the asymptotic behavior of the arrangement of empty sites and of the total displacement of all particles as well as the partial displacement of some particles when the number of sites and of the particles tend to infinite

correlation autoregressive processes with application to helicopter noise abstract this paper introduces a new class of random processes x t the autocorrelations rx t1 t2 of which satisfy a linear relation of the type r x t 1 t 2 j 1 n a j r x t 1 j t 2 j for all t1 and t2 in some interval of the time axis such random processes are denoted as correlation autoregressive this class is shown to include the familiar stationary and periodically correlated processes as well as many other both harmonizable and non harmonizable non stationary processes when a process is correlation autoregressive for all times and harmonizable its two dimensional power spectral density sx 1 2 is shown to take a particularly simple form being non zero only on lines such that 1 2 rk where the rk s are not necessarily equally spaced real roots of a characteristic function the relationship of such processes to the class of stationary processes is examined in addition the application of such processes in the analysis of typical helicopter noise signals is described

cyclo period estimation for discrete time cyclo stationary signals this paper presents a new method named as the variability method to estimate the cyclo period of a discrete time cyclo stationary signal the method is essentially based on the time varying correlation and or the time varying mean whose estimators are associated with some statistics of blocked signals a plot of variability of these statistics as a function of the blocking operator index visually reveals a periodic pattern from which the cyclo period is obtained properties of the variability method are analyzed and compared with three existing cyclo period estimation methods via simulation and real life examples

internal dla and the stefan problem generalized internal diffusion limited aggregation is a stochastic growth model on the lattice in which a finite number of sites act as poisson sources of particles which then perform symmetric random walks with an attractive zero range interaction until they reach the first site which has been visited by fewer than alpha particles at which point they stop sites on which particles are frozen constitute the occupied set we prove that in appropriate regimes the particle density has a hydrodynamic limit which is the one phase stefan problem this is then used to study the asymptotic behavior of the occupied set in two dimensions when the walks are independent with one source at the origin and alpha 1 we obtain in particular that the occupied set is asymptotically a disc of radius k sqrt t where k is the solution of exp k 2 4 pi k 2 settling a conjecture of lawler bramson and griffeath

asymptotic survival probabilities in the random saturation process we consider a model of diffusion in random media with a two way coupling i e a model in which the randomness of the medium influences the diffusing particles and where the diffusing particles change the medium in this particular model particles are injected at the origin with a time dependent rate and diffuse among random traps each trap has a finite random depth so that when it has absorbed a finite random number of particles it is saturated and it no longer acts as a trap this model comes from a problem of nuclear waste management however a very similar model has been studied recently by gravner and quastel with different tools hydrodynamic limits we compute the asymptotic behavior of the probability of survival of a particle born at some given time both in the annealed and quenched cases and show that three different situations occur depending on the injection rate for weak injection the typical survival strategy of the particle is as in sznitman and the asymptotic behavior of this survival probability behaves as if there was no saturation effect for medium injection rate the picture is closer to that of internal dla as given by lawler bramson and griffeath for large injection rates the picture is less understood except in dimension one

a problem in one dimensional diffusion limited aggregation dla and positive recurrence of markov chains we consider the following problem in one dimensional diffusion limited aggregation dla at time we have an aggregate consisting of z 0 r t with r t a positive integer we also have n i t particles at i i r t all these particles perform independent continuous time symmetric simple random walks until the first time t t at which some particle tries to jump from r t 1 to r t the aggregate is then increased to the integers in 0 r t 0 r t 1 so that r t r t 1 and all particles which were at r t 1 at time t are removed from the system the problem is to determine how fast r t grows as a function of t if we start at time 0 with r 0 0 and the n i 0 i i d poisson variables with mean 0 it is shown that if 1 then r t is of order t in a sense which is made precise it is conjectured that r t will grow linearly in t if is large enough

subdiffusive fluctuations for internal diffusion limited aggregation internal diffusion limited aggregation internal dla is a cluster model in z d where new points are added by starting random walkers at the origin and letting them run until they have found a new point to add to the cluster it has been shown that the limiting shape of internal dla clusters is spherical here we show that for d 2 the fluctuations are subdiffusive in fact that they are of order at most n 1 3 at least up to logarithmic corrections more precisely we show that for all sufficiently large n the cluster after m d n d steps covers all points in the ball of radius n n 1 3 in n 2 and is contained in the ball of radius n n 1 3 in n 4

how long does it take for internal dla to forget its initial profile internal dla is a discrete model of a moving interface on the cylinder graph mathbb z n times mathbb z a particle starts uniformly on mathbb z n times 0 and performs simple random walk on the cylinder until reaching an unoccupied site in mathbb z n times mathbb z ge 0 which it occupies forever this operation defines a markov chain on subsets of the cylinder we first show that a typical subset is rectangular with at most logarithmic fluctuations we use this to prove that two internal dla chains started from different typical subsets can be coupled with high probability by adding order n 2 log n particles for a lower bound we show that at least order n 2 particles are required to forget which of two independent typical subsets the process started from

oil and water a two type internal aggregation model we introduce a two type internal dla model which is an example of a non unary abelian network starting withn oil andn water particles at the origin the particles diuse in z according to the following rule whenever some site x2 z has at least 1 oil and at least 1 water particle present it res by sending 1 oil particle and 1 water particle each to an independent random neighbor x 1 firing continues until every site has at most one type of particles we establish the correct order for several statistics of this model and identify the scaling limit under assumption of existence

non data aided symbol rate estimation of linearly modulated signals the estimation of the symbol rate of a linearly modulated signal is addressed with special focus on low signal to noise ratio snr scenarios this problem finds application in automatic modulation classification and signal monitoring a maximum likelihood ml approach is adopted to derive practical estimators exploiting information on the cyclostationarity of the modulated signal as well as knowledge of the received signaling pulse shape the structure of the ml estimator suggests a two step estimation procedure whereby an initial coarse search determines first a neighborhood from which a subsequent fine search yields the final symbol rate estimate links between the ml approach and previous results from the literature in symbol rate estimation are established as well the proposed scheme is applicable even for small excess bandwidths at the cost of a higher complexity with respect to simpler estimators known to fail under such conditions

formation of an interface by competitive erosion we introduce a graph theoretic model of interface dynamics called competitive erosion each vertex of the graph is occupied by a particle that can be either red or blue new red and blue particles alternately get emitted from their respective bases and perform random walk on encountering a particle of the opposite color they kill it and occupy its position we prove that on the cylinder graph the product of a path and a cycle an interface spontaneously forms between red and blue and is maintained in a predictable position with high probability

blind wideband spatio temporal filtering based on higher order cyclostationarity properties in this paper a new method for blind minimum mean square error mmse spatio temporal signal filtering is proposed to obtain a blind version of the mmse filter the proposed method utilizes the signal selectivity property of the higher order cyclostationary statistics hocs exhibited by the signal of interest an accurate estimate of the transfer function of the mmse filter is obtained also in the presence of strong frequency overlapped interfering signals which would render standard stationarity based techniques ineffective the method is useful when the desired signal cannot be accurately extracted by exploiting its second order cyclostationarity properties because they are too weak and or they are shared by the interference and noise signals as well the performance analysis which is carried out by computer simulations in the case of quadrature amplitude modulated qam modulated signals with partially overlapping bands substantiates the effectiveness of the proposed method

linear prediction approach to direction estimation of cyclostationary signals in multipath environment we investigate the estimation of the directions of arrival doa of closely spaced narrowband cyclostationary signals in the presence of multipath propagation by exploiting the spatial and temporal properties of most communication signals we propose a new cyclic forward backward linear prediction fblp approach for coherent signals impinging on a uniform linear array ula in the proposed algorithm the evaluation of the cyclic array covariance matrix is avoided and the difficulty of choosing the optimal time lag parameter is alleviated as a result the proposed approach has two advantages 1 the computational load is relatively reduced and 2 the robustness of estimation is significantly improved the performance of the proposed approach is confirmed through numerical examples and it is shown that this approach is superior in resolving the closely spaced coherent signals with a small length of array data and at relatively low signal to noise ratio snr

estimating random amplitude polynomial phase signals a cyclostationary approach modeling of a class of nonstationary signals with randomly time varying amplitude and parametric polynomial phase is addressed a novel approach is proposed for the estimation of the time varying phase by exploiting the higher order cyclostationarity of these signals the method does not require nonlinear search is easy to implement and yields consistent estimates for the parameters the resulting algorithms are theoretically tolerant to a large class of noises including additive stationary non gaussian noise and any gaussian noise simulation examples supporting the theory are provided

asymptotic analysis of blind cyclic correlation based symbol rate estimators this paper considers the problem of blind symbol rate estimation of signals linearly modulated by a sequence of unknown symbols oversampling the received signal generates cyclostationary statistics that are exploited to devise symbol rate estimators by maximizing in the cyclic domain a possibly weighted sum of modulus squares of cyclic correlation estimates although quite natural the asymptotic large sample performance of this estimator has not been studied rigorously the consistency and asymptotic normality of this symbol rate estimator is established when the number of samples n converges to infinity it is shown that this estimator exhibits a fast convergence rate proportional to n sup 3 2 and it admits a simple closed form expression for its asymptotic variance this asymptotic expression enables performance analysis of the rate estimator as a function of the number of estimated cyclic correlation coefficients and the weighting matrix a justification for the high performance of the unweighted estimator in high signal to noise scenarios is also provided

asymptotic theory of mixed time averages and kth order cyclic moment and cumulant statistics we generalize parzen s 1961 analysis of asymptotically stationary processes to mixtures of deterministic stationary nonstationary and generally complex time series under certain mixing conditions expressed in terms of joint cumulant summability we show that time averages of such mixtures converge in the mean square sense to their ensemble averages we additionally show that sample averages of arbitrary orders are jointly complex normal and provide their covariance expressions these conclusions provide us with statistical tools that treat random and deterministic signals on a common framework and are helpful in defining generalized moments and cumulants of mixed processes as an important consequence we develop consistent and asymptotically normal estimators for time varying and cyclic moments and cumulants of kth order cyclostationary processes and provide computable variance expressions some examples are considered to illustrate the salient features of the analysis

sublogarithmic fluctuations for internal dla we consider internal diffusion limited aggregation in dimension larger than or equal to two this is a random cluster growth model where random walks start at the origin of the d dimensional lattice one at a time and stop moving when reaching a site that is not occupied by previous walks it is known that the asymptotic shape of the cluster is a sphere when the dimension is two or more we have shown in a previous paper that the inner resp outer fluctuations of its radius is at most of order log radius resp log2 radius using the same approach we improve the upper bound on the inner fluctuation to log radius when d is larger than or equal to three the inner fluctuation is then used to obtain a similar upper bound on the outer fluctuation