pushdown automata multiset automata and petri nets in this paper we consider various classes of infinite state automata generated by simple rewrite transition systems these classes are defined by two natural hierarchies one given by interpreting concatenation of symbols in the rewrite system as sequential composition and the other by interpreting concatenation as parallel composition in this way we provide natural definitions for commutative parallel context free automata multiset parallel or random access pushdown automata and petri nets we provide example automata which demonstrate the strictness of this hierarchy in particular we provide a proof of an earlier conjecture by moller that multiset automata form a proper subset of petri nets this result contrasts with the result of caucal for the analogous question in the sequential case where the hierarchy collapses

robust estimation of parameter for fractal inverse problem in this paper some similarity measures for fractal image compression fic are introduced which are robust against noises in the proposed methods robust estimation technique from statistics is embedded into the encoding procedure of the fractal inverse problem to find the parameters when the original image is corrupted by noises we hope that the proposed scheme is insensitive to those noises presented in the corrupted image this leads to a new concept of robust estimation of fractal inverse problem the proposed least absolute derivation lad least trimmed squares lts and wilcoxon fic are the first attempt toward the design of robust fractal image compression which can remove the noises in the encoding process the main disadvantage of the robust fic is the computational cost to overcome this drawback particle swarm optimization pso technique is utilized to reduce the searching time simulation results show that the proposed fic is robust against the outliers in the image also the pso method can effectively reduce the encoding time while retaining the quality of the retrieved image

the stochastic heat equation feynman kac formula and intermittence we study in one space dimension the heat equation with a random potential that is a white noise in space and time this equation is a linearized model for the evolution of a scalar field in a space time dependent random medium it has also been related to the distribution of two dimensional directed polymers in a random environment to the kpz model of growing interfaces and to the burgers equation with conservative noise we show how the solution can be expressed via a generalized feynman kac formula we then investigate the statistical properties the two point correlation function is explicitly computed and the intermittence of the solution is proven this analysis is carried out showing how the statistical moments can be expressed through local times of independent brownian motions

tropical combinatorics and whittaker functions we establish a fundamental connection between the geometric robinson schensted knuth rsk correspondence and gl n r whittaker functions analogous to the well known relationship between the rsk correspondence and schur functions this gives rise to a natural family of measures associated with gl n r whittaker functions which are the analogues in this setting of the schur measures on integer partitions the corresponding analogue of the cauchy littlewood identity can be seen as a generalization of an integral identity for gl n r whittaker functions due to bump and stade as an application we obtain an explicit integral formula for the laplace transform of the law of the partition function associated with a 1 dimensional directed polymer model with log gamma weights recently introduced by one of the authors

dyson s nonintersecting brownian motions with a few outliers consider n nonintersecting brownian particles on r dyson brownian motions all starting from the origin at time t 0 and forced to return to x 0 at time t 1 for large n the average mean density of particles has its support for each 0 0 does it affect the brownian fluctuations along the curve c for large n in this paper we show that no new process appears as long as one considers points y t is an element of c such that 0 infinity this kernel is closely related to one found by baik ben arous and peche in the context of multivariate statistics c 2008 wiley periodicals inc

arctic boundaries of the ice model on three bundle domains in this paper we consider the six vertex model at ice point on an arbitrary three bundle domain which is a generalization of the domain wall ice model on the square or equivalently of a uniformly random alternating sign matrix we show that this model exhibits the arctic boundary phenomenon whose boundary is given by a union of explicit algebraic curves this was originally predicted by colomo and sportiello j stat phys 164 1488 1523 2016 as one of the initial applications of a general heuristic that they introduced for locating arctic boundaries called the geometric tangent method our proof uses a probabilistic analysis of non crossing directed path ensembles to provide a mathematical justification of their tangent method heuristic in this case which might be of independent interest

huber fractal image coding based on a fitting plane recently there has been significant interest in robust fractal image coding for the purpose of robustness against outliers however the known robust fractal coding methods hfic and lad fic etc are not optimal since besides the high computational cost they use the corrupted domain block as the independent variable in the robust regression model which may adversely affect the robust estimator to calculate the fractal parameters depending on the noise level this paper presents a huber fitting plane based fractal image coding hfpfic method this method builds huber fitting planes hfps for the domain and range blocks respectively ensuring the use of an uncorrupted independent variable in the robust model on this basis a new matching error function is introduced to robustly evaluate the best scaling factor meanwhile a median absolute deviation mad about the median decomposition criterion is proposed to achieve fast adaptive quadtree partitioning for the image corrupted by salt pepper noise in order to reduce computational cost the no search method is applied to speedup the encoding process experimental results show that the proposed hfpfic can yield superior performance over conventional robust fractal image coding methods in encoding speed and the quality of the restored image furthermore the no search method can significantly reduce encoding time and achieve less than 2 0 s for the hfpfic with acceptable image quality degradation in addition we show that combined with the mad decomposition scheme the hfp technique used as a robust method can further reduce the encoding time while maintaining image quality

fractal image denoising over the past decade there has been significant interest in fractal coding for the purpose of image compression however applications of fractal based coding to other aspects of image processing have received little attention we propose a fractal based method to enhance and restore a noisy image if the noisy image is simply fractally coded a significant amount of the noise is suppressed however one can go a step further and estimate the fractal code of the original noise free image from that of the noisy image based upon a knowledge or estimate of the variance of the noise assumed to be zero mean stationary and gaussian the resulting fractal code yields a significantly enhanced and restored representation of the original noisy image the enhancement is consistent with the human visual system where extra smoothing is performed in flat and low activity regions and a lower degree of smoothing is performed near high frequency components e g edges of the image we find that for significant noise variance spl sigma spl ges 20 the fractal based scheme yields results that are generally better than those obtained by the lee filter which uses a localized first order filtering process similar to fractal schemes we also show that the lee filter and the fractal method are closely related

a polynomial algorithm for deciding bisimilarity of normed context free processes the previous best upper bound on the complexity of deciding bisimilarity between normed context free processes due to huynh and tian is that the problem lies in the second level of the polynomial hierarchy their algorithm guesses a proof of equivalence and validates this proof in polynomial time using oracles freely answering questions which are in np in this paper we improve on this result by presenting a polynomial time algorithm which solves this problem as a corollary we have a polynomial algorithm for the equivalence problem for simple context free grammars

scaling for a one dimensional directed polymer with boundary conditions we study a 1 1 dimensional directed polymer in a random environment on the integer lattice with log gamma distributed weights among directed polymers this model is special in the same way as the last passage percolation model with exponential or geometric weights is special among growth models namely both permit explicit calculations with appropriate boundary conditions the polymer with log gamma weights satisfies an analogue of burke s theorem for queues building on this we prove the conjectured values for the fluctuation exponents of the free energy and the polymer path in the case where the boundary conditions are present and both endpoints of the polymer path are fixed for the polymer without boundary conditions and with either fixed or free endpoint we get the expected upper bounds on the exponents

solving the kpz equation we introduce a new concept of solution to the kpz equation which is shown to extend the classical cole hopf solution this notion provides a factorisation of the cole hopf solution map into a universal measurable map from the probability space into an explicitly described auxiliary metric space composed with a new solution map that has very good continuity properties the advantage of such a formulation is that it essentially provides a pathwise notion of a solution together with a very detailed approximation theory in particular our construction completely bypasses the cole hopf transform thus laying the groundwork for proving that the kpz equation describes the uctuations of systems in the kpz universality class as a corollary of our construction we obtain very detailed new regularity results about the solution as well as its derivative with respect to the initial condition other byproducts of the proof include an explicit approximation to the stationary solution of the kpz equation a well posedness result for the fokker planck equation associated to a particle diusing in a rough space time dependent potential and a new periodic homogenisation result for the heat equation with a space time periodic potential one ingredient in our construction is an example of a non gaussian rough path such that the area process of its natural approximations needs to be renormalised by a diverging term for the approximations to converge

ccs expressions finite state processes and three problems of equivalence abstract we examine the computational complexity of testing finite state processes for equivalence in milner s calculus of communicating systems ccs the equivalence problems in ccs are presented as refinements of the familiar problem of testing whether two nondeterministic finite automata nfa are equivalent i e accept the same language three notions of equivalence proposed for ccs are investigated namely observational equivalence strong observational equivalence and failure equivalence we show that observational equivalence can be tested in polynomial time as defined in ccs observational equivalence is the limit of a sequence of successively finer equivalence relations k where 1 is nondeterministic finite automaton equivalence we prove that for each fixed k deciding k is pspace complete we show that strong observational equivalence can be decided in polynomial time by reducing it to generalized partitioning a new combinatorial problem of independent interest finally we demonstrate that testing for failure equivalence is pspace complete even for a very restricted type of process

gues and queues consider the process d k k 1 2 given by b i being independent standard brownian motions this process describes the limiting behavior near the edge in queues in series totally asymmetric exclusion processes or oriented percolation the problem of finding the distribution of d was posed in gw the main result of this paper is that the process d has the law of the process of the largest eigenvalues of the main minors of an infinite random matrix drawn from gaussian unitary ensemble

limit theorems for height fluctuations in a class of discrete space and time growth models we introduce a class of one dimensional discrete space discrete time stochastic growth models described by a height function ht x with corner initialization we prove with one exception that the limiting distribution function of ht x suitably centered and normalized equals a fredholm determinant previously encountered in random matrix theory in particular in the universal regime of large x and large t the limiting distribution is the fredholm determinant with airy kernel in the exceptional case called the critical regime the limiting distribution seems not to have previously occurred the proofs use the dual rsk algorithm gessel s theorem the borodin okounkov identity and a novel rigorous saddle point analysis in the fixed x large t regime we find a brownian motion representation this model is equilvalent to the seppalainen johansson model hence some of our results are not new but the proofs are

o connell s process as a vicious brownian motion vicious brownian motion is a diffusion scaling limit of fisher s vicious walk model which is a system of brownian particles in one dimension such that if two motions meet they kill each other we consider the vicious brownian motions conditioned never to collide with each other and call it noncolliding brownian motion this conditional diffusion process is equivalent to the eigenvalue process of the hermitian matrix valued brownian motion studied by dyson j math phys 3 1191 1962 recently o connell ann probab to be published introduced a generalization of the noncolliding brownian motion by using the eigenfunctions the whittaker functions of the quantum toda lattice in order to analyze a directed polymer model in 1 1 dimensions we consider a system of one dimensional brownian motions with a long ranged killing term as a generalization of the vicious brownian motion and construct the o connell process as a conditional process of the killing brownian motions to survive forever

brownian gibbs property for airy line ensembles consider a collection of n brownian bridges b i n n to mathbb r b i n b i n 0 1 i n conditioned not to intersect the edge scaling limit of this system is obtained by taking a weak limit as n of the collection of curves scaled so that the point 0 21 2 n is fixed and space is squeezed horizontally by a factor of n 2 3 and vertically by n 1 3 if a parabola is added to each of the curves of this scaling limit an x translation invariant process sometimes called the multi line airy process is obtained we prove the existence of a version of this process which we call the airy line ensemble in which the curves are almost surely everywhere continuous and non intersecting this process naturally arises in the study of growth processes and random matrix ensembles as do related processes with wanderers and outliers we formulate our results to treat these relatives as well note that the law of the finite collection of brownian bridges above has the property called the brownian gibbs property of being invariant under the following action select an index 1 k n and erase b k on a fixed time interval a b n n then replace this erased curve with a new curve on a b according to the law of a brownian bridge between the two existing endpoints a b k a and b b k b conditioned to intersect neither the curve above nor the one below we show that this property is preserved under the edge scaling limit and thus establish that the airy line ensemble has the brownian gibbs property an immediate consequence of the brownian gibbs property is a confirmation of the prediction of m prahofer and h spohn that each line of the airy line ensemble is locally absolutely continuous with respect to brownian motion we also obtain a proof of the long standing conjecture of k johansson that the top line of the airy line ensemble minus a parabola attains its maximum at a unique point this establishes the asymptotic law of the transversal fluctuation of last passage percolation with geometric weights our probabilistic approach complements the perspective of exactly solvable systems which is often taken in studying the multi line airy process and readily yields several other interesting properties of this process

a fast fractal image coding based on kick out and zero contrast conditions a fast algorithm for fractal image coding based on a single kick out condition and the zero contrast prediction is proposed in this paper the single kick out condition can avoid a large number of range domain block matches when finding the best matched domain block an efficient method for zero contrast prediction is also proposed which can determine whether the contrast factor for a domain block is zero or not and compute the corresponding difference between the range block and the transformed domain block efficiently and exactly the proposed algorithm can achieve the same reconstructed image quality as the exhaustive search and can greatly reduce the required computation or runtime in addition this algorithm does not need any pre processing step or additional memory for its implementation and can combine with other fast fractal algorithms to further improve the speed experimental results show that the runtime is reduced by about 50 of that of the exhaustive search method when combined with the dct inner product algorithm the required runtime for the algorithm can be further reduced by about 50 the proposed algorithm was also compared to two other fast fractal algorithms experimental results also show that our algorithm achieves a better efficiency and requires a much smaller amount of memory for implementation

iterated function systems and the global construction of fractals iterated function systems i f ss are introduced as a unified way of generating a broad class of fractals these fractals are often attractors for i f ss and occur as the supports of probability measures associated with functional equations the existence of certain p balanced measures for i f ss is established and these measures are uniquely characterized for hyperbolic i f ss the hausdorff besicovitch dimension for some attrac tors of hyperbolic i f ss is estimated with the aid of p balanced measures what appears to be the broadest framework for the exactly computable moment theory of p balanced measures that of linear i f ss and of probabilistic mixtures of iterated riemann surfaces is presented this extensively generalizes earlier work on orthogonal polynomials on julia sets an example is given of fractal reconstruction with the use of linear i f ss and moment theory

transversal fluctuations of the asep stochastic six vertex model and hall littlewood gibbsian line ensembles we consider the asep and the stochastic six vertex model started with step initial data after a long time t it is known that the one point height function fluctuations for these systems are of order t1 3 we prove the kpz prediction of t2 3 scaling in space namely we prove tightness and brownian absolute continuity of all subsequential limits as t goes to infinity of the height function with spatial coordinate scaled by t2 3 and fluctuations scaled by t1 3 the starting point for proving these results is a connection discovered recently by borodin bufetov wheeler between the stochastic six vertex height function and the hall littlewood process a certain measure on plane partitions interpreting this process as a line ensemble with a gibbsian resampling invariance we show that the one point tightness of the top curve can be propagated to the tightness of the entire curve

crossover distributions at the edge of the rarefaction fan we consider the weakly asymmetric limit of simple exclusion process with drift to the left starting from step bernoulli initial data with so that macroscopically one has a rarefaction fan we study the fluctuations of the process observed along slopes in the fan which are given by the hopf cole solution of the kardar parisi zhang kpz equation with appropriate initial data for slopes strictly inside the fan the initial data is a dirac delta function and the one point distribution functions have been computed in comm pure appl math 64 2011 466 537 and nuclear phys b 834 2010 523 542 at the edge of the rarefaction fan the initial data is one sided brownian we obtain a new family of crossover distributions giving the exact one point distributions of this process which converge as t to those of the airy a2 bm process as an application we prove moment and large deviation estimates for the equilibrium hopf cole solution of kpz these bounds rely on the apparently new observation that the fkg inequality holds for the stochastic heat equation finally via a feynman kac path integral the kpz equation also governs the free energy of the continuum directed polymer and thus our formula may also be interpreted in those terms

paths in weyl chambers and random matrices baryshnikov 4 and gravner tracy widom 15 have shown that the largest eigenvalue of a random matrix of the g u e of order d has the same distribution as

a multi layer extension of the stochastic heat equation motivated by recent developments on solvable directed polymer models we define a multi layer extension of the stochastic heat equation involving non intersecting brownian motions by developing a connection with darboux transformations and the two dimensional toda equations we conjecture a markovian evolution in time for this multi layer process as a first step in this direction we establish an analogue of the karlin mcgregor formula for the stochastic heat equation and use it to prove a special case of this conjecture

transition between airy1 and airy2 processes and tasep fluctuations we consider the totally asymmetric simple exclusion process a model in the kpz universality class we focus on the fluctuations of particle positions starting with certain deterministic initial conditions for large time t one has regions with constant and linearly decreasing density the fluctuations on these two regions are given by the airy1 and airy2 processes whose one point distributions are the goe and gue tracy widom distributions of random matrix theory in this paper we analyze the transition region between these two regimes and obtain the transition process its one point distribution is a new interpolation between goe and gue edge distributions 2007 wiley periodicals inc

fast fractal image encoding based on adaptive search this paper presents a new adaptive search approach to reduce the computational complexity of fractal encoding a simple but very efficient adaptive necessary condition is introduced to exclude a large number of unqualified domain blocks so as to speed up fractal image compression furthermore we analyzed an unconventional affine parameter that has better properties than the conventional luminance offset specifically we formulated an optimal bit allocation scheme for the simultaneous quantizations of the usual scaling and the aforementioned unconventional affine parameter experiments on standard images showed that our adaptive search method yields superior performance over conventional fractal encoding

renormalization fixed point of the kpz universality class the one dimensional kardar parisi zhang universality class is believed to describe many types of evolving interfaces which have the same characteristic scaling exponents these exponents lead to a natural renormalization rescaling on the space of such evolving interfaces we introduce and describe the renormalization fixed point of the kardar parisi zhang universality class in terms of a random nonlinear semigroup with stationary independent increments and via a variational formula furthermore we compute a plausible formula the exact transition probabilities using replica bethe ansatz the semigroup is constructed from the airy sheet a four parameter space time field which is the airy 2 process in each of its two spatial coordinates minimizing paths through this field describe the renormalization group fixed point of directed polymers in a random potential at present the results we provide do not have mathematically rigorous proofs and they should at most be considered proposals

directed polymers and the quantum toda lattice we characterize the law of the partition function of a brownian directed polymer model in terms of a diffusion process associated with the quantum toda lattice the proof is via a multidimensional generalization of a theorem of matsumoto and yor concerning exponential functionals of brownian motion it is based on a mapping which can be regarded as a geometric variant of the rsk correspondence

from duality to determinants for q tasep and asep we prove duality relations for two interacting particle systems the q deformed totally asymmetric simple exclusion process q tasep and the asymmetric simple exclusion process asep expectations of the duality functionals correspond to certain joint moments of particle locations or integrated currents respectively duality implies that they solve systems of odes these systems are integrable and for particular step and half stationary initial data we use a nested contour integral ansatz to provide explicit formulas for the systems solutions and hence also the moments we form laplace transform like generating functions of these moments and via residue calculus we compute two different types of fredholm determinant formulas for such generating functions for asep the first type of formula is new and readily lends itself to asymptotic analysis as necessary to reprove gue tracy widom distribution fluctuations for asep while the second type of formula is recognizable as closely related to tracy and widom s asep formula comm math phys 279 2008 815 844 j stat phys 132 2008 291 300 comm math phys 290 2009 129 154 j stat phys 140 2010 619 634 for q tasep both formulas coincide with those computed via borodin and corwin s macdonald processes probab theory related fields 2014 158 225 400 both q tasep and asep have limit transitions to the free energy of the continuum directed polymer the logarithm of the solution of the stochastic heat equation or the hopf cole solution to the kardar parisi zhang equation thus q tasep and asep are integrable discretizations of these continuum objects the systems of odes associated to their dualities are deformed discrete quantum delta bose gases and the procedure through which we pass from expectations of their duality functionals to characterizing generating functions is a rigorous version of the replica trick in physics

image coding based on a fractal theory of iterated contractive image transformations the author proposes an independent and novel approach to image coding based on a fractal theory of iterated transformations the main characteristics of this approach are that i it relies on the assumption that image redundancy can be efficiently exploited through self transformability on a block wise basis and ii it approximates an original image by a fractal image the author refers to the approach as fractal block coding the coding decoding system is based on the construction for an original image to encode of a specific image transformation a fractal code which when iterated on any initial image produces a sequence of images that converges to a fractal approximation of the original it is shown how to design such a system for the coding of monochrome digital images at rates in the range of 0 5 1 0 b pixel the fractal block coder has performance comparable to state of the art vector quantizers

weak type 1 1 estimates for heat kernel maximal functions on lie groups for a lie group g with left invariant haar measure and associated lebesgue spaces lp g we consider the heat kernels pt t o arising from a right invariant laplacian a on g that is u t pt f solves the heat equation a ot a u 0 with initial condition u o f we establish weak type 1 1 estimates for the maximal operator xf ji f supt 0 pt f 1 and for related hardy littlewood maximal operators in a variety of contexts namely for groups of polynomial growth and for a number of classes of iwasawa an groups we also study the local maximal operator x0 of sup0 o t ipt f i and related hardy littlewood operators for all lie groups

a note on the complexity of deciding bisimilarity of normed unary processes we give nc1 reduction of bisimulation equivalence for general normed context free processes to the same problem for normed unary context free processes

on deciding readiness and failure equivalences for processes in this paper we study the complexity of deciding readiness and failure equivalences for finite state processes and recursively defined processes specified by normed context free grammars cfgs in greibach normal form gnf the results are as follows 1 readiness and failure equivalences for processes specified by normed gnf cfgs are both undecidable for this class of processes the regularity problem with respect to failure or readiness equivalence is also undecidable moreover all these undecidability results hold even for locally unary processes in the unary case these problems become decidable in fact they are p2 complete we also show that with respect to bisimulation equivalence the regularity for processes specified by normed gnf cfgs is nl complete 2 readiness and failure equivalences for finite state processes are pspace complete this holds even for locally unary finite state processes these two equivalences are co np complete for unary finite state processes further for acyclic finite state processes readiness and failure equivalences are co np complete and they are nl complete in the unary case 3 for finite tree processes we show that finite trace readiness and failure equivalences are all l complete further the results remain true for the unary case our results provide a complete characterization of the computational complexity of deciding readiness and failure equivalences for several important classes of processes

kpz line ensemble for each t ge 1 we construct an mathbb n indexed ensemble of random continuous curves with three properties 1 the lowest indexed curve is distributed as the time t hopf cole solution to the kardar parisi zhang kpz stochastic partial differential equation with narrow wedge initial data 2 the entire ensemble satisfies a resampling invariance which we call the mathbf h brownian gibbs property with mathbf h x e x 3 increments of the lowest indexed curve when centered by t 24 and scaled down vertically by t 1 3 and horizontally by t 2 3 remain uniformly absolutely continuous i e have tight radon nikodym derivatives with respect to brownian bridges as time t goes to infinity this construction uses as inputs the diffusion that o connell discovered ann probab 40 437 458 2012 in relation to the o connell yor semi discrete brownian polymer the convergence result of moreno flores et al in preparation of the lowest indexed curve of that diffusion to the solution of the kpz equation with narrow wedge initial data and the one point distribution formula proved by amir et al commun pure appl math 64 466 537 2011 for the solution of the kpz equation with narrow wedge initial data we provide four main applications of this construction 1 uniform as t goes to infinity brownian absolute continuity of the time t solution to the kpz equation with narrow wedge initial data even when scaled vertically by t 1 3 and horizontally by t 2 3 2 universality of the t 1 3 one point vertical fluctuation scale for the solution of the kpz equation with general initial data 3 concentration in the t 2 3 scale for the endpoint of the continuum directed random polymer 4 exponential upper and lower tail bounds for the solution at fixed time of the kpz equation with general initial data

fractal wavelet image denoising revisited the essence of fractal image denoising is to predict the fractal code of a noiseless image from its noisy observation from the predicted fractal code one can generate an estimate of the original image we show how well fractal wavelet denoising predicts parent wavelet subetres of the noiseless image the performance of various fractal wavelet denoising schemes e g fixed partitioning quadtree partitioning is compared to that of some standard wavelet thresholding methods we also examine the use of cycle spinning in fractal based image denoising for the purpose enhancing the denoised estimates our experimental results show that these fractal based image denoising methods are quite competitive with standard wavelet thresholding methods for image denoising finally we compare the performance of the pixel and wavelet based fractal denoising schemes

deciding bisimilarity of normed context free processes is in σ p 2 existing decision algorithms for bisimulation equivalence for normed context free processes require at least exponential time we develop a p2 a subclass of pspace algorithm for deciding bisimulation equivalence for normed context free processes

probability distribution of the free energy of the continuum directed random polymer in 1 1 dimensions we consider the solution of the stochastic heat equation tz d 1 2 x zz p w with delta function initial condition z t d0 x dixd0 whose logarithm with appropriate normalization is the free energy of the con tinuum directed polymer or the hopf cole solution of the kardar parisi zhang equation with narrow wedge initial conditions we obtain explicit formulas for the one dimensional marginal distributions the crossover distributions which interpolate between a standard gaussian dis tribution small time and the gue tracy widom distribution large time the proof is via a rigorous steepest descent analysis of the tracy widom formula for the asymmetric simple exclusion process with antishock initial data which is shown to converge to the continuum equations in an appropriate weakly asymmetric limit the limit also describes the crossover behavior between the symmetric and asymmetric exclusion processes 2010 wiley periodicals inc

the one dimensional kpz equation and its universality class our understanding of the one dimensional kpz equation alias noisy burgers equation has advanced substantially over the past 5 years we provide a non technical review where we limit ourselves to the stochastic pde and lattice type models approximating it

stochastic burgers and kpz equations from particle systems we consider two strictly related models a solid on solid interface growth model and the weakly asymmetric exclusion process both on the one dimensional lattice it has been proven that in the diffusive scaling limit the density field of the weakly asymmetric exclusion process evolves according to the burgers equation and the fluctuation field converges to a generalized ornstein uhlenbeck process we analyze instead the density fluctuations beyond the hydrodynamical scale and prove that their limiting distribution solves the non linear burgers equation with a random noise on the density current for the solid on solid model we prove that the fluctuation field of the interface profile if suitably rescaled converges to the kardar parisi zhang equation this provides a microscopic justification of the so called kinetic roughening i e the non gaussian fluctuations in some non equilibrium processes our main tool is the cole hopf transformation and its microscopic version we also develop a mathematical theory for the macroscopic equations

study on huber fractal image compression in this paper a new similarity measure for fractal image compression fic is introduced in the proposed huber fractal image compression hfic the linear huber regression technique from robust statistics is embedded into the encoding procedure of the fractal image compression when the original image is corrupted by noises we argue that the fractal image compression scheme should be insensitive to those noises presented in the corrupted image this leads to a new concept of robust fractal image compression the proposed hfic is one of our attempts toward the design of robust fractal image compression the main disadvantage of hfic is the high computational cost to overcome this drawback particle swarm optimization pso technique is utilized to reduce the searching time simulation results show that the proposed hfic is robust against outliers in the image also the pso method can effectively reduce the encoding time while retaining the quality of the retrieved image

lower tail of the kpz equation we provide the first tight bounds on the lower tail probability of the one point distribution of the kardar parisi zhang kpz equation with narrow wedge initial data our bounds hold for all sufficiently large times t and demonstrates a crossover between superexponential decay with exponent 52 and leading prefactor 415 t1 3 for tail depth greater than t2 3 and exponent 3 with leading prefactor at least 112 for tail depth less than t2 3

anomalous shock fluctuations in tasep and last passage percolation models we consider the totally asymmetric simple exclusion process with initial conditions and or jump rates such that shocks are generated if the initial condition is deterministic then the shock at time t will have a width of order t 1 3 we determine the law of particle positions in the large time limit around the shock in a few models in particular we cover the case where at both sides of the shock the process of the particle positions is asymptotically described by the airy 1 process the limiting distribution is a product of two distribution functions which is a consequence of the fact that at the shock two characteristics merge and of the slow decorrelation along the characteristics we show that the result generalizes to generic last passage percolation models

infinite dimensional stochastic differential equations for dyson s model in this paper we show the strong existence and the pathwise uniqueness of an infinite dimensional stochastic differential equation sde corresponding to the bulk limit of dyson s brownian motion for all beta ge 1 our construction applies to an explicit and general class of initial conditions including the lattice configuration x i mathbb z and the sine process we further show the convergence of the finite to infinite dimensional sde this convergence concludes the determinantal formula of katori and tanemura commun math phys 293 2 469 497 2010 for the solution of this sde at beta 2

on the chaotic character of the stochastic heat equation before the onset of intermitttency we consider a nonlinear stochastic heat equation tu 1 xxu u xtw where xtw denotes space time white noise and r r is lipschitz continuous we establish that at every xed time t 0 the global behavior of the solution depends in a critical manner on the structure of the initial function u0 under suitable technical conditions on u0 and supx2rut x is a s nite when u0 has compact support whereas with probability one lim supjxj 1ut x logjxj 1 6 0 when u0 is bounded uniformly away from zero the mentioned sensitivity to the initial data of the stochastic heat equation is a way to state that the solution to the stochastic heat equation is chaotic at xed times well before the onset of intermittency

on the chaotic character of the stochastic heat equation ii consider the stochastic heat equation partial t u varkappa 2 delta u sigma u dot f where the solution u u t x is indexed by t x in 0 infty times bf r d and dot f is a centered gaussian noise that is white in time and has spatially correlated coordinates we analyze the large x fixed t behavior of the solution u in different regimes thereby study the effect of noise on the solution in various cases among other things we show that if the spatial correlation function f of the noise is of riesz type that is f x propto x alpha then the fluctuation exponents of the solution are psi for the spatial variable and 2 psi 1 for the time variable where psi 2 4 alpha moreover these exponent relations hold as long as alpha in 0 d wedge 2 that is precisely when dalang s theory dalang electron j probab 4 paper no 6 29 1999 implies the existence of a solution to our stochastic pde these findings bolster earlier physical predictions kardar et al phys rev lett 58 20 889 892 1985 kardar and zhang phys rev lett 58 20 2087 2090 1987

transversal fluctuations for increasing subsequences on the plane consider a realization of a poisson process in 2 with intensity 1 and take a maximal up right path from the origin to n n consisting of line segments between the points where maximal means that it contains as many points as possible the number of points in such a path has fluctuations of order n where 1 3 bdj here we show that typical deviations of a maximal path from the diagonal x y is of order n with 2 3 this is consistent with the scaling identity 2 1 which is believed to hold in many random growth models

deciding bisimulation and trace equivalences for systems with many identical processes abstract in the study of process semantics trace equivalence and bisimulation equivalence constitute the two extremes of the so called linear time branching time spectrum in this paper we study the complexity and decidability issues of deciding trace and bisimulation equivalences for the model of systems with many identical processes with respect to various interprocess communication structures in our model each system consists of an arbitrary number of identical finite state processes using milner s calculus of communicating systems ccs as the style of interprocess communication as it turns out deciding trace and bisimulation equivalences are undecidable for star like and linear systems whereas the two problems are complete for pspace and ptime respectively for fully connected systems