persistence of gaussian processes non summable correlations suppose the auto correlations of real valued centered gaussian process z cdot are non negative and decay as rho s t for some rho cdot regularly varying at infinity of order alpha in 1 0 with i rho t int 0 t rho s ds its primitive we show that the persistence probabilities decay rate of log mathbb p sup t in 0 t z t 0 is precisely of order t i rho t log i rho t thereby closing the gap between the lower and upper bounds of newell and rosenblatt ann math stat 33 1306 1313 1962 which stood as such for over fifty years we demonstrate its usefulness by sharpening recent results of sakagawa adv appl probab 47 146 163 2015 about the dependence on d of such persistence decay for the langevin dynamics of certain nabla phi interface models on mathbb z d

random polynomials having few or no real zeros consider a polynomial of large degree n whose coefficients are independent identically distributed nondegenerate random variables having zero mean and finite moments of all orders we show that such a polynomial has exactly k real zeros with probability n b o 1 as n through integers of the same parity as the fixed integer k 0 in particular the probability that a random polynomial of large even degree n has no real zeros is n b o 1 the finite positive constant b is characterized via the centered stationary gaussian process of correlation function sech t 2 the value of b depends neither on k nor upon the specific law of the coefficients under an extra smoothness assumption about the law of the coefficients with probability n b o 1 one may specify also the approximate locations of the k zeros on the real line the constant b is replaced by b 2 in case the i i d coefficients have a nonzero mean

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

delocalization of two dimensional random surfaces with hard core constraints we study the fluctuations of random surfaces on a two dimensional discrete torus the random surfaces we consider are defined via a nearest neighbor pair potential which we require to be twice continuously differentiable on a possibly infinite interval and infinity outside of this interval no convexity assumption is made and we include the case of the so called hammock potential when the random surface is uniformly chosen from the set of all surfaces satisfying a lipschitz constraint our main result is that these surfaces delocalize having fluctuations whose variance is at least of order log n where n is the side length of the torus we also show that the expected maximum of such surfaces is of order at least log n the main tool in our analysis is an adaptation to the lattice setting of an algorithm of richthammer who developed a variant of a mermin wagner type argument applicable to hard core constraints we rely also on the reflection positivity of the random surface model the result answers a question mentioned by brascamp et al on the hammock potential and a question of velenik

a solution procedure for second order difference equations and its application to electromagnetic wave diffraction in a wedge shaped region this paper proposes an efficient solution procedure for second order functional difference equations and outlines this procedure through investigating electromagnetic wave diffraction by a canonical structure comprising an impedance wedge and an impedance sheet bisecting the exterior region of the wedge applying the sommerfeld malyuzhinets technique to the original boundary value problem yields a linear system of equations for the two coupled spectral functions eliminating one spectral function leads to a second order difference equation for the other the chief steps in this work consist of transforming the second order equation into a simpler one by making use of a generalized malyuzhinets function and in expressing the solution to the latter in an integral form with help of the so called s integrals from this integral expression one immediately obtains a fredholm equation of the second kind for points on the imaginary axis of the complex plane solving this integral equation by means of the well known quadrature method enables us to calculate the sought for spectral function inside the basic strip via an interpolation formula and outside it via an analytic extension the second spectral function is obtained through its dependence upon the first the uniform asymptotic solution which is of particular interest in the geometrical theory of diffraction follows by evaluating the sommerfeld integrals in the far field from the exact one several examples demonstrate the efficiency and accuracy of the proposed procedure as well as typical behaviour of the far field solutions for such a canonical problem of diffraction theory

on tests for normality the problem of deciding whether a sample of a random field was generated by a gaussian distribution is considered based on extensions of large deviation estimates due to m d donsker and s r s varadhan 1985 a test that is optimal in a generalized neyman pearson sense is proposed this test turns out to depend on properties of the entropy of gaussian processes and does not depend on cumulant computations

persistence probability of random weyl polynomial in this paper we obtain the persistence exponents of random weyl polynomials in both cases the nonnegative axis and the whole real axis our result confirms the predictions given by schehr and majumdar j stat phys 132 2 235 273 2008 in the nonnegative axis case dembo and mukherjee ann probab 43 1 85 118 2015 gave an upper bound for the persistence exponent by considering the persistence probability on a suitable interval our main contribution is to prove this upper bound is the exact exponent and to extend to the whole real axis case

random walks among time increasing conductances heat kernel estimates for any graph having a suitable uniform poincare inequality and volume growth regularity we establish two sided gaussian transition density estimates and parabolic harnack inequality for constant speed continuous time random walks evolving via time varying uniformly elliptic conductances provided the vertex conductances i e reversing measures increase in time such transition density upper bounds apply for discrete time uniformly lazy walks with the matching lower bounds holding once the parabolic harnack inequality is proved

pde with random coefficients and euclidean field theory in this paper a new proof of an identity of giacomin olla and spohn is given the identity relates the 2 point correlation function of a euclidean field theory to the expectation of the green s function for a pde with random coefficients the euclidean field theory is assumed to have convex potential an inequality of brascamp and lieb therefore implies gaussian bounds on the fourier transform of the 2 point correlation function by an application of results from random pde the previously mentioned identity implies pointwise gaussian bounds on the 2 point correlation function

large deviations for almost markovian processes large deviation theorems for the empirical distribution of almost markovian processes are proven relative entropy identifies the rate function and its definition depends only on the process

infinite lattice systems of interacting diffusion processes existence and regularity properties generalized stochastic gradient systems for infinite lattice models are investigated the allowed strength of the interaction depends on the dimension of the lattice the semigroup of transition probabilities is constructed and its regularity properties are also discussed some results of doss and royer 2 are improved

large deviation principle with generated pseudo measures contemporary large deviation theory uses various approaches one of possible recent approaches is based on the idempotent sup measure and related integrals based on operations sup and the usual product in this paper the large deviation convergence of a sequence of generated pseudo measures to sup decomposable measure is introduced the main result of the paper gives a necessary condition for introduced convergence

persistence exponents for fluctuating interfaces numerical and analytic results for the exponent ensuremath theta describing the decay of the first return probability of an interface to its initial height are obtained for a large class of linear langevin equations the models are parametrized by the dynamic roughness exponent ensuremath beta with 0l ensuremath beta l1 for ensuremath beta frac 1 2 the time evolution is markovian using simulations of solid on solid models of the discretized continuum equations as well as of the associated zero dimensional stationary gaussian process we address two problems the return of an initially flat interface and the return to an initial state with fully developed steady state roughness the two problems are shown to be governed by different exponents for the steady state case we point out the equivalence to fractional brownian motion which has a return exponent ensuremath theta s 1 ensuremath ensuremath beta the exponent ensuremath theta 0 for the flat initial condition appears to be nontrivial we prove that ensuremath theta 0 ensuremath rightarrow ensuremath infty for ensuremath beta ensuremath rightarrow 0 ensuremath theta 0 g ensuremath theta s for ensuremath beta l frac 1 2 and ensuremath theta 0 l ensuremath theta s for ensuremath beta g frac 1 2 and calculate ensuremath theta 0 s perturbatively to first order in an expansion around the markovian case ensuremath beta frac 1 2 using the exact result ensuremath theta s 1 ensuremath ensuremath beta accurate upper and lower bounds on ensuremath theta 0 can be derived which show in particular that ensuremath theta 0 g 1 ensuremath ensuremath beta 2 ensuremath beta for small ensuremath beta

on the correlation for kac like models in the convex case the aim of this paper is to stu the behavior asm tends to of a family of measures exp m x dx m on m where m is a potential on m which is a perturbation in a suitable sense of the harmonic potential j x j 2

large deviations for noninteracting infinite particle systems a large deviation property is established for noninteracting infinite particle systems previous large deviation results obtained by the authors involved a singlei function because the cases treated always involved a unique invariant measure for the process in the context of this paper there is an infinite family of invariant measures and a corresponding infinite family ofi functions governing the large deviations

edge universality of beta ensembles we prove the edge universality of the beta ensembles for any beta ge 1 provided that the limiting spectrum is supported on a single interval and the external potential is fancyscript c 4 and regular we also prove that the edge universality holds for generalized wigner matrices for all symmetry classes moreover our results allow us to extend bulk universality for beta ensembles from analytic potentials to potentials in class fancyscript c 4

detection of gauss markov random fields with nearest neighbor dependency the problem of hypothesis testing against independence for a gauss markov random field gmrf is analyzed assuming an acyclic dependency graph an expression for the log likelihood ratio of detection is derived assuming random placement of nodes over a large region according to the poisson or uniform distribution and nearest neighbor dependency graph the error exponent of the neyman pearson detector is derived using large deviations theory the error exponent is expressed as a dependency graph functional and the limit is evaluated through a special law of large numbers for stabilizing graph functionals the exponent is analyzed for different values of the variance ratio and correlation it is found that a more correlated gmrf has a higher exponent at low values of the variance ratio whereas the situation is reversed at high values of the variance ratio

strict convexity of the free energy for a class of non convex gradient models we consider a gradient interface model on the lattice with interaction potential which is a non convex perturbation of a convex potential we show using a one step multiple scale analysis the strict convexity of the surface tension at high temperature this is an extension of funaki and spohn s result 8 where the strict convexity of potential was crucial in their proof

existence and stability for fokker planck equations with log concave reference measure we study markov processes associated with stochastic differential equations whose non linearities are gradients of convex functionals we prove a general result of existence of such markov processes and a priori estimates on the transition probabilities the main result is the following stability property if the associated invariant measures converge weakly then the markov processes converge in law the proofs are based on the interpretation of a fokker planck equation as the steepest descent flow of the relative entropy functional in the space of probability measures endowed with the wasserstein distance

optimal node density for detection in energy constrained random networks the problem of optimal node density maximizing the neyman pearson detection error exponent subject to a constraint on average per node energy consumption is analyzed the spatial correlation among the sensor measurements is incorporated through a gauss markov random field gmrf model with euclidean nearest neighbor dependency graph a constant density deployment of sensors under the uniform or poisson distribution is assumed it is shown that the optimal node density crucially depends on the ratio between the measurement variances under the two hypotheses and displays a threshold behavior below the threshold value of the variance ratio the optimal node density tends to infinity under any feasible average energy constraint on the other hand when the variance ratio is above the threshold the optimal node density is the minimum value at which it is feasible to process and deliver the likelihood ratio sufficient statistic of the sensor measurements to the fusion center in this regime of the variance ratio an upper bound on the optimal node density based on a proposed 2 approximation fusion scheme and a lower bound based on the minimum spanning tree are established under an alternative formulation where the energy consumption per unit area is constrained the optimal node density is shown to be strictly finite for all values of the variance ratio and bounds on this optimal node density are provided

motion by mean curvature from the ginzburg landau interface model we consider the scalar field t with a reversible stochastic dynamics which is defined by the standard dirichlet form relative to the gibbs measure with formal energy the potential v is even and strictly convex we prove that under a suitable large scale limit the t field becomes deterministic such that locally its normal velocity is proportional to its mean curvature except for some anisotropy effects as an essential input we prove that for every tilt there is a unique shift invariant ergodic gibbs measure for the field

a multiscale hp fem for 2d photonic crystal bands a multiscale generalised hp finite element method msfem for time harmonic wave propagation in bands of locally periodic media of large but finite extent e g photonic crystal phc bands is presented the method distinguishes itself by its size robustness i e to achieve a prescribed error its computational effort does not depend on the number of periods the proposed method shows this property for general incident fields including plane waves incident at a certain angle to the infinite crystal surface and at frequencies in and outside of the bandgap of the phc the proposed msfem is based on a precomputed problem adapted multiscale basis this basis incorporates a set of complex bloch modes the eigenfunctions of the infinite phc which are modulated by macroscopic piecewise polynomials on a macroscopic fe mesh the multiscale basis is shown to be efficient for finite phc bands of any size provided that boundary effects are resolved with a simple macroscopic boundary layer mesh the msfem constructed by combing the multiscale basis inside the crystal with some exterior discretisation is a special case of the generalised finite element method g fem for the rapid evaluation of the matrix entries we introduce a size robust algorithm for integrals of quasi periodic micro functions and polynomial macro functions size robustness of the present msfem in both the number of basis functions and the computation time is verified in extensive numerical experiments

large deviations for gibbs random fields a large deviation principle for gibbs random fields on zd is proven and a corresponding large deviations proof of the gibbs variational formula is given a generalization of the lanford theory of large deviations is also obtained

green s functions for elliptic and parabolic equations with random coefficients ii this paper is concerned with linear parabolic partial differential equations in divergence form and their discrete analogues it is assumed that the coefficients of the equation are stationary random variables random in both space and time the green s functions for the equations are then random variables regularity properties for expectation values of green s functions are obtained in particular it is shown that the expectation value is a continuously differentiable function in the space variable whose derivatives are bounded by the corresponding derivatives of the green s function for the heat equation similar results are obtained for the related finite difference equations this paper generalises results of a previous paper which considered the case when the coefficients are constant in time but random in space

approximation of the effective conductivity of ergodic media by periodization this paper is concerned with the approximation of the effective conductivity a associated to an elliptic operator xa x x where for x d d 1 a x is a bounded elliptic random symmetric d d matrix and takes value in an ergodic probability space x writing an x the periodization of a x on the torus tdn of dimension d and side n we prove that for almost all we extend this result to non symmetric operators x a e x x corresponding to diffusions in ergodic divergence free flows a is d d elliptic symmetric matrix and e x an ergodic skew symmetric matrix and to discrete operators corresponding to random walks on d with ergodic jump rates

how much information can one get from a wireless ad hoc sensor network over a correlated random field new large deviations results that characterize the asymptotic information rates for general d dimensional d d stationary gaussian fields are obtained by applying the general results to sensor nodes on a two dimensional 2 d lattice the asymptotic behavior of ad hoc sensor networks deployed over correlated random fields for statistical inference is investigated under a 2 d hidden gauss markov random field model with symmetric first order conditional autoregression and the assumption of no in network data fusion the behavior of the total obtainable information nats and energy efficiency nats j defined as the ratio of total gathered information to the required energy is obtained as the coverage area node density and energy vary when the sensor node density is fixed the energy efficiency decreases to zero with rate theta area 1 2 and the per node information under fixed per node energy also diminishes to zero with rate o nt 1 3 as the number nt of network nodes increases by increasing the coverage area as the sensor spacing dn increases the per node information converges to its limit d with rate d radic dn e alphadn for a given diffusion rate alpha when the coverage area is fixed and the node density increases the per node information is inversely proportional to the node density as the total energy et consumed in the network increases the total information obtainable from the network is given by o loget for the fixed node density and fixed coverage case and by theta et 2 3 for the fixed per node sensing energy and fixed density and increasing coverage case

stochastic analysis rough path analysis and fractional brownian motions in this paper we show by using dyadic approximations the existence of a geometric rough path associated with a fractional brownian motion with hurst parameter greater than 1 4 using the integral representation of fractional brownian motions we furthermore obtain a skohorod integral representation of the geometric rough path we constructed by the results in ly1 a stochastic integration theory may be established for fractional brownian motions and strong solutions and a wong zakai type limit theorem for stochastic differential equations driven by fractional brownian motions can be deduced accordingly the method can actually be applied to a larger class of gaussian processes with covariance functions satisfying a simple decay condition

fluctuations for a φ interface model with repulsion from a wall we consider a interface model on a one dimensional lattice with repulsion from a hard wall we suppose that the repulsion is of the form c 1 where c 0 and denotes the height of the interface from the wall we prove convergence of the equilibrium fluctuations around the hydrodynamic limit to the solution of a spde with singular drift if c 0 the system becomes the funaki olla interface model with reflection at the wall whose equilibrium fluctuations converge to the solution of a spde with reflection we give a new proof of this result using the characterization of such solution as the diffusion generated by an infinite dimensional dirichlet form obtained in a previous paper our method is based on a study of integration by parts formulae w r t the equilibrium measure of the interface model and allows to avoid the proof of the so called boltzmann gibbs principle we also obtain convergence of finite dimensional distributions of non equilibrium fluctuations around the stationary hydrodynamic limit 0

generalized sommerfeld integral and diffraction in an angle shaped domain with a radial perturbation the sommerfeld integral enabled one to solve various diffraction problems in angle shaped domains the basic goal of the present paper is to demonstrate a generalized form of the famous sommerfeld integral the kernel of the traditional sommerfeld integral is replaced by the solution of a scattering problem the latter hint leads to the possibility of representing solutions for a more general class of diffraction problems in an angle shaped domain with the radial perturbation of the boundary or and with the presence of a radially symmetric refraction index in the stationary wave helmholtz equation the approach is demonstrated in the simplest situation of diffraction in an angle shaped domain with the centrally circular with respect to the angle vertex perturbation of the perfectly conducting boundary

stochastic calculus for fractional brownian motion with hurst exponent h a rough path method by analytic extension the d dimensional fractional brownian motion fbm for short b t b 1 t b d t t r with hurst exponent 0 1 is a d dimensional centered self similar gaussian process with covariance e b i s b i t 1 2 i j lsl 2 ltl 2 t s 2 the long standing problem of defining a stochastic integration with respect to fbm and the related problem of solving stochastic differential equations driven by fbm has been addressed successfully by several different methods although in each case with a restriction on the range of either d or the case corresponds to the usual stochastic integration with respect to brownian motion while most computations become singular when gets under various threshhold values due to the growing irregularity of the trajectories as 0 we provide here a new method valid for any d and for 1 4 by constructing an approximation e t e 0 of fbm which allows to define iterated integrals and then applying the geometric rough path theory the approximation relies on the definition of an analytic process z on the cut plane z c r of which fbm appears to be a boundary value and allows to understand very precisely the well known see 5 but as yet a little mysterious divergence of levy s area for 1 4

scaling limit for a class of gradient fields with nonconvex potentials we consider gradient fields x x d whose law takes the gibbs boltzmann form z 1 exp x y v v x where the sum runs over nearest neighbors we assume that the potential v admits the representation v log d exp 1 2 2 where is a positive measure with compact support in 0 hence the potential v is symmetric but nonconvex in general while for strictly convex v s the translation invariant ergodic gradient gibbs measures are completely characterized by their tilt a nonconvex potential as above may lead to several ergodic gradient gibbs measures with zero tilt still every ergodic zero tilt gradient gibbs measure for the potential v above scales to a gaussian free field

a characterisation of the gaussian free field we prove that a random distribution in two dimensions which is conformally invariant and satisfies a natural domain markov property is a multiple of the gaussian free field this result holds subject only to a fourth moment assumption

an explicit schilder type theorem for super brownian motions like ordinary brownian motion super brownian motion a central object in the theory of superprocesses is a universal object arising in a variety of settings schilder type theorems and cramer type theorems are two of the major topics for large deviation theory a schilder type which is also a cramer type sample large deviation for super brownian motions with a good rate function represented by a variation formula was established in 1993 and 1994 since then there have been very valuable contributions for giving an affirmative answer to the question of whether this sample large deviation holds with an explicit good rate function in this paper thanks to previous results on this issue and the brownian snake we establish such a large deviation for nonzero finite initial measures 2010 wiley periodicals inc

central limit theorem for additive functionals of reversible markov processes and applications to simple exclusions we prove a functional central limit theorem for additive functionals of stationary reversible ergodic markov chains under virtually no assumptions other than the necessary ones we use these results to study the asymptotic behavior of a tagged particle in an infinite particle system performing simple excluded random walk

the large deviation principle for hypermixing processes the large deviation principle of donsker and varadhan type is proved under certain hypotheses on the base stationary process some examples of processes satisfying those hypotheses are also given

large deviations and concentration properties for ϕ interface models we consider the massless field with zero boundary conditions outside d n d d n n d a suitable subset of d i e the continuous spin gibbs measure n on d n with hamiltonian given by h x y x y 1 v x y and x 0 for x d n c the interaction v is taken to be strictly convex and with bounded second derivative this is a standard effective model for a d 1 dimensional interface represents the height of the interface over the base d n due to the choice of scaling of the base we scale the height with the same factor by setting n n we study various concentration and relaxation properties of the family of random surfaces n and of the induced family of gradient fields n n as the discretization step 1 n tends to zero n in particular we prove a large deviation principle for n and show that the corresponding rate function is given by d u x dx where is the surface tension of the model this is a multidimensional version of the sample path large deviation principle we use this result to study the concentration properties of n under the volume constraint i e the constraint that 1 n d x dn n x stays in a neighborhood of a fixed volume v 0 and the hard wall constraint i e n x 0 for all x this is therefore a model for a droplet of volume v lying above a hard wall we prove that under these constraints the field n of rescaled heights concentrates around the solution of a variational problem involving the surface tension as it would be predicted by the phenomenological theory of phase boundaries our principal result however asserts local relaxation properties of the gradient field n n to the corresponding extremal gibbs states thus our approach has little in common with traditional large deviation techniques and is closer in spirit to hydrodynamic limit type of arguments the proofs have both probabilistic and analytic aspects essential analytic tools are p estimates for elliptic equations and the theory of young measures on the side of probability tools a central role is played by the helffer sjostrand 31 pde representation for continuous spin systems which we rewrite in terms of random walk in random environment and by recent results of t funaki and h spohn 25 on the structure of gradient fields

large deviations and variational principle for harmonic crystals we consider massless gaussian fields with covariance related to the green function of a long range random walk on d these are viewed as gibbs measures for a linear quadratic interaction we establish thermodynamic identities and prove a version of gibbs variational principle showing that translation invariant gibbs measures are characterized as minimizers of the relative entropy density we then study the large deviations of the empirical field of a gibbs measure we show that a weak large deviation principle holds at the volume order with rate given by the relative entropy density

equilibrium fluctuations for nabla_ varphi interface model we study the large scale space time fluctuations of an interface which is modeled by a massless scalar field with reversible langevin dynamics for a strictly convex interaction potential we prove that on a large space time scale these fluctuations are governed by an infinite dimensional ornstein uhlenbeck process its effective diffusion type covariance matrix is characterized through a variational formula

a solution of the isomorphism problem for circulant graphs the isomorphism problem for circulant graphs cayley graphs over the cyclic group which has been open since 1967 is completely solved in this paper the main result of the paper gives an efficient isomorphism criterion for circulant graphs of arbitrary order this result also solves an isomorphism problem for colored circulant graphs and some classes of cyclic codes

quantification of ergodicity in stochastic homogenization optimal bounds via spectral gap on glauber dynamics we study quantitatively the effective large scale behavior of discrete elliptic equations on the lattice mathbb z d with random coefficients the theory of stochastic homogenization relates the random stationary and ergodic field of coefficients with a deterministic matrix of effective coefficients this is done via the corrector problem which can be viewed as a highly degenerate elliptic equation on the infinite dimensional space of admissible coefficient fields in this contribution we develop new quantitative methods for the corrector problem based on the assumption that ergodicity holds in the quantitative form of a spectral gap estimate w r t a glauber dynamics on coefficient fields as it is the case for independent and identically distributed coefficients as a main result we prove an optimal decay in time of the semigroup associated with the corrector problem i e of the generator of the process called random environment as seen from the particle as a corollary we recover existence of stationary correctors in dimensions d 2 and prove new optimal estimates for regularized versions of the corrector in dimensions d ge 2 we also give a self contained proof of a new estimate on the gradient of the parabolic variable coefficient green s function which is a crucial analytic ingredient in our approach as an application of these results we prove the first and optimal estimates for the approximation of the homogenized coefficients by the popular periodization method in case of independent and identically distributed coefficients

pattern densities in non frozen planar dimer models in this paper we introduce a family of observables for the dimer model on a bi periodic bipartite planar graph called pattern density fields we study the scaling limit of these objects for non frozen gibbs measures of the dimer model and prove that they converge to a linear combination of a derivative of the gaussian massless free field and an independent white noise

extinction time of non markovian self similar processes persistence annihilation of jumps and the frechet distribution we start by providing an explicit characterization and analytical properties including the persistence phenomena of the distribution of the extinction time mathbb t of a class of non markovian self similar stochastic processes with two sided jumps that we introduce as a stochastic time change of markovian self similar processes for a suitably chosen time change we observe for classes with two sided jumps the following surprising facts on the one hand all the mathbb t s within a class have the same law which we identify in a simple form for all classes and reduces in the spectrally positive case to the frechet distribution on the other hand each of its distribution corresponds to the law of an extinction time of a single markov process without positive jumps leaving the interpretation that the time change has annihilated the effect of positive jumps the example of the non markovian processes associated to levy stable processes is detailed

large deviations for stationary gaussian processes in their previous work on large deviations the authors always assumed the base process to be markovian whereas here they consider the base process to be stationary gaussian similar large deviation results are obtained under natural hypotheses on the spectral density function of the base process a rather explicit formula for the entropy involved is also obtained

convection diffusion equation with space time ergodic random flow we prove the homogenization of convection diffusion in a time dependent ergodic incompressible random flow which has a bounded stream matrix and a constant mean drift we also prove two variational formulas for the effective diffusivity as a consequence we obtain both upper and lower bounds on the effective diffusivity

neyman pearson detection of gauss markov signals in noise closed form error exponentand properties the performance of neyman pearson detection of correlated random signals using noisy observations is considered using the large deviations principle the performance is analyzed via the error exponent for the miss probability with a fixed false alarm probability using the state space structure of the signal and observation model a closed form expression for the error exponent is derived using the innovations approach and the connection between the asymptotic behavior of the optimal detector and that of the kalman filter is established the properties of the error exponent are investigated for the scalar case it is shown that the error exponent has distinct characteristics with respect to correlation strength for signal to noise ratio snr spl ges 1 the error exponent is monotonically decreasing as the correlation becomes strong whereas for snr 1 there is an optimal correlation that maximizes the error exponent for a given snr

correlation structure of the corrector in stochastic homogenization recently the quantification of errors in the stochastic homogenization of divergence form operators has witnessed important progress our aim now is to go beyond error bounds and give precise descriptions of the effect of the randomness in the large scale limit this paper is a first step in this direction our main result is to identify the correlation structure of the corrector in dimension 33 and higher this correlation structure is similar to but different from that of a gaussian free field

on estimating the derivatives of symmetric diffusions in stationary random environment with applications to ϕ interface model we consider diffusions on d or random walks on d in a random environment which is stationary in space and in time and with symmetric and uniformly elliptic coefficients we show existence and holder continuity of second space derivatives and time derivatives for the annealed kernels of such diffusions and give estimates for these derivatives in the case of random walks these estimates are applied to the ginzburg landau interface model

no zero crossings for random polynomials and the heat equation consider random polynomial ni 0aixi of independent mean zero normal coefficients ai whose variance is a regularly varying function in i of order we derive general criteria for continuity of persistence exponents for centered gaussian processes and use these to show that such polynomial has no roots in 0 1 with probability n b o 1 and no roots in 1 with probability n b0 o 1 hence for n even it has no real roots with probability n 2b 2b0 o 1 here b 0 when 1 and otherwise b 0 is independent of the detailed regularly varying variance function and corresponds to persistence probabilities for an explicit stationary gaussian process of smooth sample path further making precise the solution d x t to the d dimensional heat equation initiated by a gaussian white noise d x 0 we confirm that the probability of d x t 0 for all t 1 t is t b o 1 for d 2 1

evolution problems in spaces of probability measures abstract this is a short survey paper on the application of monge s theory of optimal mass transportation to evolution problems of a gradient type in the case when the natural state space is the space of probability measures this occurs for instance for fokker planck equations and optimal mass transportation methods provide in this setting very general existence and stability results

scaling limits of weakly asymmetric interfaces we consider three models of evolving interfaces intimately related to the weakly asymmetric simple exclusion process with n particles on a finite lattice of 2n sites our model 1 defines an evolving bridge on 0 1 our model 1 w an evolving excursion on 0 1 while our model 2 consists of an evolving pair of non crossing bridges on 0 1 based on the observation that the invariant measures of the dynamics depend on the area under or between the interface s we characterise the scaling limits of the invariant measures when the asymmetry of the exclusion process scales like n frac 3 2 then we show that the scaling limits of the dynamics themselves are expressed in terms of variants of the stochastic heat equation in particular in model 1 w we obtain the well studied reflected stochastic heat equation introduced by nualart and pardoux probab theory relat fields 93 1 77 89 1992