asymptotics in asep with step initial condition in previous work the authors considered the asymmetric simple exclusion process on the integer lattice in the case of step initial condition particles beginning at the positive integers there it was shown that the probability distribution for the position of an individual particle is given by an integral whose integrand involves a fredholm determinant here we use this formula to obtain three asymptotic results for the positions of these particles in one an apparently new distribution function arises and in another the distribution function f2 arises the latter extends a result of johansson on tasep to asep and hence proves kpz universality for asep with step initial condition

aspects of total variation regularized l1 function approximation the total variation based image denoising model of rudin osher and fatemi phys d 60 1992 pp 259 268 has been generalized and modified in many ways in the literature one of these modifications is to use the l1 norm as the fidelity term we study the interesting consequences of this modification especially from the point of view of geometric properties of its solutions it turns out to have interesting new implications for data driven scale selection and multiscale image decomposition

dynamics of a tagged particle in the asymmetric exclusion process with the step initial condition the one dimensional totally asymmetric simple exclusion process tasep is considered we study the time evolution property of a tagged particle in the tasep with the step initial condition calculated is the multi time joint distribution function of its position using the relation of the dynamics of the tasep to the schur process we show that the function is represented as the fredholm determinant we also study the scaling limit the universality of the largest eigenvalue in the random matrix theory is realized in the limit when the hopping rates of all particles are the same it is found that the joint distribution function converges to that of the airy process after the time at which the particle begins to move on the other hand when there are several particles with small hopping rate in front of a tagged particle the limiting process changes at a certain time from the airy process to the process of the largest eigenvalue in the hermitian multi matrix model with external sources

direct evaluation of large deviation functions we introduce a numerical procedure to evaluate directly the probabilities of large deviations of physical quantities such as current or density that are local in time the large deviation functions are given in terms of the typical properties of a modified dynamics and since they no longer involve rare events can be evaluated efficiently and over a wider ranges of values we illustrate the method with the current fluctuations of the totally asymmetric exclusion process and with the work distribution of a driven lorentz gas

current fluctuations of the one dimensional symmetric simple exclusion process with step initial condition for the symmetric simple exclusion process on an infinite line we calculate exactly the fluctuations of the integrated current qt during time t through the origin when in the initial condition the sites are occupied with density a on the negative axis and with density b on the positive axis all the cumulants of qt grow like sqrt t in the range where q t sim sqrt t the decay exp qt3 t of the distribution of qt is non gaussian our results are obtained using the bethe ansatz and several identities derived recently by tracy and widom for exclusion processes on the infinite line

fluctuation properties of the tasep with periodic initial configuration we consider the joint distributions of particle positions for the continuous time totally asymmetric simple exclusion process tasep they are expressed as fredholm determinants with a kernel defining a signed determinantal point process we then consider certain periodic initial conditions and determine the kernel in the scaling limit this result has been announced first in a letter by one of us sasamoto in j phys a 38 l549 l556 2005 and here we provide a self contained derivation connections to last passage directed percolation and random matrices are also briefly discussed

finite time current probabilities in the asymmetric exclusion process on a ring we calculate the time dependent probability distribution of current through a selected bond in the totally asymmetric exclusion process with periodic boundary conditions we derive a general formula for the probability that the integrated current exceeds a given value n at the moment of time t the formula is written in a form of a contour integral of a determinant of a toeplitz matrix transforming the determinant expression we obtain a generalization of the known formula derived by johansson for the infinite one dimensional lattice to check the general formula we consider the specific case corresponding to the probability of a minimal non zero current for this case we get an explicit analytical expression and analyze its asymptotics

formulas for asep with two sided bernoulli initial condition for the asymmetric simple exclusion process t on the integer lattice with two sided bernoulli initial condition we derive exact formulas for the following quantities 1 p t x 1 the probability that site x is occupied at time t 2 the correlation function p t x 1 0 0 1 3 the distribution function for qt the total flux across 0 at time t and its exponential generating function

a multilevel algorithm for simultaneously denoising and deblurring images in this paper we develop a fast multilevel algorithm for simultaneously denoising and deblurring images under the total variation regularization although much effort has been devoted to developing fast algorithms for the numerical solution and the denoising problem was satisfactorily solved fast algorithms for the combined denoising and deblurring model remain to be a challenge recently several successful studies of approximating this model and subsequently finding fast algorithms were conducted which have partially solved this problem the aim of this paper is to generalize a fast multilevel denoising method to solving the minimization model for simultaneously denoising and deblurring our new idea is to overcome the complexity issue by a detailed study of the structured matrices that are associated with the blurring operator a fast algorithm can then be obtained for directly solving the variational model supporting numerical experiments on gray scale images are presented

non equilibrium current fluctuations in stochastic lattice gases we study current fluctuations in lattice gases in the macroscopic limit extending the dynamic approach for density fluctuations developed in previous articles more precisely we establish a large deviation principle for a space time fluctuation j of the empirical current with a rate functional i j we then estimate the probability of a fluctuation of the average current over a large time interval this probability can be obtained by solving a variational problem for the functional i we discuss several possible scenarios interpreted as dynamical phase transitions for this variational problem they actually occur in specific models we finally discuss the time reversal properties of i and derive a fluctuation relationship akin to the gallavotti cohen theorem for the entropy production

entropy of open lattice systems we investigate the behavior of the gibbs shannon entropy of the stationary nonequilibrium measure describing a one dimensional lattice gas of l sites with symmetric exclusion dynamics and in contact with particle reservoirs at different densities in the hydrodynamic scaling limit l the leading order o l behavior of this entropy has been shown by bahadoran to be that of a product measure corresponding to strict local equilibrium we compute the first correction which is o 1 the computation uses a formal expansion of the entropy in terms of truncated correlation functions for this system the k th such correlation is shown to be o l k 1 this entropy correction depends only on the scaled truncated pair correlation which describes the covariance of the density field it coincides in the large l limit with the corresponding correction obtained from a gaussian measure with the same covariance

hydrodynamics and large deviation for simple exclusion processes we prove the hydrodynamical limit for weakly asymmetric simple exclusion processes a large deviation property with respect to this limit is established for the symmetric case we treat also the situation where a slow reaction creation and annihilation of particles is present

variational image registration by a total fractional order variation model in this paper a new framework of nonlocal deformation in non rigid image registration is presented it is well known that many non rigid image registration techniques may lead to unsteady deformation e g not one to one if the dissimilarity between the reference and template images is too large we present a novel variational framework of the total fractional order variation to derive the underlying fractional euler lagrange equations and a numerical implementation combining the semi implicit update and conjugate gradients cg solution to solve the nonlinear systems numerical experiments show that the new registration not only produces accurate and smooth solutions but also allows for a large rigid alignment the evaluations of the new model demonstrate substantial improvements in accuracy and robustness over the conventional image registration approaches

shape fluctuations and random matrices we study a certain random growth model in two dimensions closely related to the one dimensional totally asymmetric exclusion process the results show that the shape fluctuations appropriately scaled converges in distribution to the tracy widom largest eigenvalue distribution for the gaussian unitary ensemble gue

on deformation of poisson manifolds of hydrodynamic type we study a class of deformations of infinite dimensional poisson manifolds of hydrodynamic type which are of interest in the theory of frobenius manifolds we prove two results first we show that the second cohomology group of these manifolds in the poisson lichnerowicz cohomology is essentially trivial then we prove a conjecture of b dubrovin about the triviality of homogeneous formal deformations of the above manifolds

on bi hamiltonian deformations of exact pencils of hydrodynamic type in this paper we are interested in nontrivial bi hamiltonian deformations of the poisson pencil deformations are generated by a sequence of vector fields x2 x3 x4 where each xk is homogeneous of degree k with respect to a grading induced by rescaling constructing recursively the vector fields xk one obtains two types of relations involving their unknown coefficients one set of linear relations and an other one which involves quadratic relations we prove that the set of linear relations has a geometric meaning using miura quasitriviality the set of linear relations expresses the tangency of the vector fields xk to the symplectic leaves of 1 and this tangency condition is equivalent to the exactness of the pencil moreover extending the results of lorenzoni p 2002 j geom phys 44 331 75 we construct the nontrivial deformations of the poisson pencil up to the eighth order in the deformation parameter showing therefore that deformations are unobstructed and that both poisson structures are polynomial in the derivatives of u up to that order

a nonlinear primal dual method for total variation based image restoration we present a new method for solving total variation tv minimization problems in image restoration the main idea is to remove some of the singularity caused by the nondifferentiability of the quantity nabla u in the definition of the tv norm before we apply a linearization technique such as newton s method this is accomplished by introducing an additional variable for the flux quantity appearing in the gradient of the objective function which can be interpreted as the normal vector to the level sets of the image u our method can be viewed as a primal dual method as proposed by conn and overton a primal dual interior point method for minimizing a sum of euclidean norms preprint 1994 and andersen ph d thesis odense university denmark 1995 for the minimization of a sum of euclidean norms in addition to possessing local quadratic convergence experimental results show that the new method seems to be globally convergent

current distribution and random matrix ensembles for an integrable asymmetric fragmentation process we calculate the time evolution of a discrete time fragmentation process in which clusters of particles break up and reassemble and move stochastically with size dependent rates in the continuous time limit the process turns into the totally asymmetric simple exclusion process only pieces of size 1 break off a given cluster we express the exact solution of the master equation for the process in terms of a determinant which can be derived using the bethe ansatz from this determinant we compute the distribution of the current across an arbitrary bond which after appropriate scaling is given by the distribution of the largest eigenvalue of the gaussian unitary ensemble of random matrices this result confirms universality of the scaling form of the current distribution in the kpz universality class and suggests that there is a link between integrable particle systems and random matrix ensembles

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

frobenius manifolds and central invariants for the drinfeld sokolov bihamiltonian structures the drinfeld sokolov construction associates a hierarchy of bihamiltonian integrable systems with every untwisted affine lie algebra we compute the complete sets of invariants of the related bihamiltonian structures with respect to the group of miura type transformations

limiting shapes of ising droplets ising fingers and ising solitons we examine the evolution of an ising ferromagnet endowed with zero temperature single spin flip dynamics a large droplet of one phase in the sea of the opposite phase eventually disappears an interesting behavior occurs in the intermediate regime when the droplet is still very large compared to the lattice spacing but already very small compared to the initial size in this regime the shape of the droplet is essentially deterministic fluctuations are negligible in comparison with characteristic size in two dimensions the shape is also universal that is independent of the initial shape we analytically determine the limiting shape of the ising droplet on the square lattice when the initial state is a semi infinite stripe of one phase in the sea of the opposite phase it evolves into a finger which translates along its axis we determine the limiting shape and the velocity of the ising finger on the square lattice an analog of the ising finger on the cubic lattice is the translating ising soliton we show that far away from the tip the cross section of the ising soliton coincides with the limiting shape of the two dimensional ising droplet and we determine a relation between the cross section area the distance from the tip and the velocity of the soliton

hamiltonian pdes deformations integrability solutions we review recent classification results on the theory of systems of nonlinear hamiltonian partial differential equations with one spatial dimension including a perturbative approach to the integrability theory of such systems and discuss universality conjectures describing critical behaviour of solutions to such systems

the asymmetric simple exclusion process an integrable model for non equilibrium statistical mechanics the asymmetric simple exclusion process asep plays the role of a paradigm in non equilibrium statistical mechanics we review exact results for the asep obtained by the bethe ansatz and put emphasis on the algebraic properties of this model the bethe equations for the eigenvalues of the markov matrix of the asep are derived from the algebraic bethe ansatz using these equations we explain how to calculate the spectral gap of the model and how global spectral properties such as the existence of multiplets can be predicted an extension of the bethe ansatz leads to an analytic expression for the large deviation function of the current in the asep that satisfies the gallavotti cohen relation finally we describe some variants of the asep that are also solvable by the bethe ansatz

universal cumulants of the current in diffusive systems on a ring we calculate exactly the first cumulants of the integrated current and of the activity which is the total number of changes of configurations of the symmetric simple exclusion process on a ring with periodic boundary conditions our results indicate that for large system sizes the large deviation functions of the current and of the activity take a universal scaling form with the same scaling function for both quantities this scaling function can be understood either by an analysis of bethe ansatz equations or in terms of a theory based on fluctuating hydrodynamics or on the macroscopic fluctuation theory of bertini de sole gabrielli jona lasinio and landim

symmetric exclusion process with a localized source we investigate the growth of the total number of particles in a symmetric exclusion process driven by a localized source the average total number of particles entering an initially empty system grows with time as t in one dimension t ln t in two dimensions and linearly in higher dimensions in one and two dimensions the leading asymptotic behaviors for the average total number of particles are independent of the intensity of the source we also discuss fluctuations of the total number of particles and determine the asymptotic growth of the variance in one dimension

dispersive deformations of hamiltonian systems of hydrodynamic type in 2 1 dimensions abstract we develop a theory of integrable dispersive deformations of 2 1 dimensional hamiltonian systems of hydrodynamic type following the scheme proposed by dubrovin and his collaborators in 1 1 dimensions our results show that the multi dimensional situation is far more rigid and generic hamiltonians are not deformable as an illustration we discuss a particular class of two component hamiltonian systems establishing the triviality of first order deformations and classifying hamiltonians possessing nontrivial deformations of the second order

current fluctuations in one dimensional diffusive systems with a step initial density profile we show how to apply the macroscopic fluctuation theory mft of bertini de sole gabrielli jona lasinio and landim to study the current fluctuations of diffusive systems with a step initial condition we argue that one has to distinguish between two ways of averaging the annealed and the quenched cases depending on whether we let the initial condition fluctuate or not although the initial condition is not a steady state the distribution of the current satisfies a symmetry very reminiscent of the fluctuation theorem we show how the equations of the mft can be solved in the case of non interacting particles the symmetry of these equations can be used to deduce the distribution of the current for several other models from its knowledge derrida and gerschenfeld in j stat phys 136 1 15 2009 for the symmetric simple exclusion process in the range where the integrated current q t sim sqrt t we show that the non gaussian decay exp q t 3 t of the distribution of q t is generic

a fredholm determinant representation in asep in previous work tracy and widom in commun math phys 279 815 844 2008 the authors found integral formulas for probabilities in the asymmetric simple exclusion process asep on the integer lattice the dynamics are uniquely determined once the initial state is specified in this note we restrict our attention to the case of step initial condition with particles at the positive integers and consider the distribution function for the mth particle from the left in tracy and widom commun math phys 279 815 844 2008 an infinite series of multiple integrals was derived for the distribution in this note we show that the series can be summed to give a single integral whose integrand involves a fredholm determinant we use this determinant representation to derive non rigorously at this writing a scaling limit

an iterative lagrange multiplier method for constrained total variation based image denoising various effective algorithms have been proposed in the past two decades for nonlinear pdes arising from the unconstrained total variation based image denoising problem regularizing the total variation constrained minimization model such algorithms can be used to obtain a satisfactory result as long as a suitable regularization parameter balancing the trade off between a good fit to the data and a regular solution is given however it is generally difficult to obtain a suitable regularization parameter without which restored images can be unsatisfactory if it is too large then the resulting solution is still contaminated by noise while if too small the solution is a poor approximation of the true noise free solution to provide an automatic method for the regularization parameter when the noise level is known a priori one way is to address the coupled karush kuhn tucker kkt systems from the constrained total variation optimization problem so far much less work has been done on this problem this

current fluctuations in the exclusion process and bethe ansatz we use the bethe ansatz to derive analytical expressions for the current statistics in the asymmetric exclusion process with both forward and backward jumps the bethe equations are highly coupled and this fact has impeded their use in deriving exact results for finite systems we overcome this technical difficulty by reformulating bethe equations into a one variable polynomial problem akin to the functional bethe ansatz the perturbative solution of this equation leads to the cumulants of the current we calculate here the first two orders and derive exact formulae for the mean value of the current and its fluctuations

diffusion in concentrated lattice gases the diffusion of many particles on a lattice is an example of a correlated random walk process recently the waiting time distributions for two consecutive jumps of a tagged particle have been determined numerically and the time dependent correlations analyzed in detail the information over these two consecutive jumps is used to determine the position and velocity autocorrelation functions and very satisfactory results are obtained for three dimensional lattices however the information of the two consecutive jumps is insufficient when the jump rate of the tagged particle is large compared to that of the other particles and this approximation fails completely in one dimension for the linear chain another approximation which accounts for correlations over all jumps is compared with the numerical simulations

adapting to unknown smoothness via wavelet shrinkage abstract we attempt to recover a function of unknown smoothness from noisy sampled data we introduce a procedure sureshrink that suppresses noise by thresholding the empirical wavelet coefficients the thresholding is adaptive a threshold level is assigned to each dyadic resolution level by the principle of minimizing the stein unbiased estimate of risk sure for threshold estimates the computational effort of the overall procedure is order n log n as a function of the sample size n sureshrink is smoothness adaptive if the unknown function contains jumps then the reconstruction essentially does also if the unknown function has a smooth piece then the reconstruction is essentially as smooth as the mother wavelet will allow the procedure is in a sense optimally smoothness adaptive it is near minimax simultaneously over a whole interval of the besov scale the size of this interval depends on the choice of mother wavelet we know from a previous paper by the authors that traditional smoot

bihamiltonian cohomology of kdv brackets using spectral sequences techniques we compute the bihamiltonian cohomology groups of the pencil of poisson brackets of dispersionless kdv hierarchy in particular this proves a conjecture of liu and zhang about the vanishing of such cohomology groups

limit processes for tasep with shocks and rarefaction fans we consider the totally asymmetric simple exclusion process tasep with two sided bernoulli initial condition i e with left density and right density we study the associated height function whose discrete gradient is given by the particle occurrences macroscopically one has a deterministic limit shape with a shock or a rarefaction fan depending on the values of we characterize the large time scaling limit of the multipoint fluctuations as a function of the densities and of the different macroscopic regions moreover using a slow decorrelation phenomena the results are extended from fixed time to the whole space time except along the some directions the characteristic solutions of the related burgers equation where the problem is still open

a limit theorem for the position of a tagged particle in a simple exclusion process on montre l extremalite d une mesure invariante pour le processus n a partir d une particule etiquetee et on utilise les proprietes d ergodicite du processus initial pour montrer que la position suit une loi des grands nombres

on high order denoising models and fast algorithms for vector valued images variational techniques for gray scale image denoising have been deeply investigated for many years however little research has been done for the vector valued denoising case and the very few existent works are all based on total variation regularization it is known that total variation models for denoising gray scaled images suffer from staircasing effect and there is no reason to suggest this effect is not transported into the vector valued models high order models on the contrary do not present staircasing in this paper we introduce three high order and curvature based denoising models for vector valued images their properties are analyzed and a fast multigrid algorithm for the numerical solution is provided ams subject classifications 68u10 65f10 65k10

exact solution of the master equation for the asymmetric exclusion process using the bethe ansatz we obtain the exact solution of the master equation for the totally asymmetric exclusion process on an infinite one dimensional lattice we derive explicit expressions for the conditional probabilitiesp x1 xn t y1 yn 0 of findingn particles on lattices sitesx1 xn at timet with initial occupationy1 yn at timet 0

exact eigenspectrum of the symmetric simple exclusion process on the complete complete bipartite and related graphs we show that the infinitesimal generator of the symmetric simple exclusion process recast as a quantum spin ferromagnetic heisenberg model can be solved by elementary techniques on the complete complete bipartite and related multipartite graphs some of the resulting infinitesimal generators are formally identical to homogeneous as well as mixed higher spins models the degeneracies of the eigenspectra are described in detail and the clebsch gordan machinery needed to deal with the arbitrary spin s representations of the su 2 is briefly developed we mention in passing how our results fit within the related questions of a ferromagnetic ordering of energy levels and a conjecture according to which the spectral gaps of the random walk and the interchange process on finite simple graphs must be equal

integral formulas for the asymmetric simple exclusion process in this paper we obtain general integral formulas for probabilities in the asymmetric simple exclusion process asep on the integer lattice mathbb z with nearest neighbor hopping rates p to the right and q 1 p to the left for the most part we consider an n particle system but for certain of these formulas we can take the n to infty limit first we obtain for the n particle system a formula for the probability of a configuration at time t given the initial configuration for this we use bethe ansatz ideas to solve the master equation extending a result of schutz for the case n 2 the main results of the paper derived from this are integral formulas for the probability for given initial configuration that the mth left most particle is at x at time t in one of these formulas we can take the n to infty limit and it gives the probability for an infinite system where the initial configuration is bounded on one side for the special case of the totally asymmetric simple exclusion process tasep our formulas reduce to the known ones

bihamiltonian hierarchies in 2d topological field theory at one loop approximation we compute the genus one correction to the integrable hierarchy describing coupling to gravity of a 2d topological field theory the bihamiltonian structure of the hierarchy is given by a classical w algebra we compute the central charge of this algebra we also express the generating function of elliptic gromov witten invariants via tau function of the isomonodromy deformation problem arising in the theory of wdvv equations of associativity

on the convergence of the lagged diffusivity fixed point method in total variation image restoration in this paper we show that the lagged diffusivity fixed point algorithm introduced by vogel and oman in siam j sci comput 17 1996 pp 227 238 to solve the problem of total variation denoising proposed by rudin osher and fatemi in phys d 60 1992 pp 259 268 is a particular instance of a class of algorithms introduced by voss and eckhardt in computing 25 1980 pp 243 251 whose origins can be traced back to weiszfeld s original work for minimizing a sum of euclidean lengths tohoku math j 43 1937 pp 355 386 there have recently appeared several proofs for the convergence of this algorithm g aubert et al technical report 94 01 informatique signaux et systemes de sophia antipolis 1994 a chambolle and p l lions technical report 9509 ceremade 1995 and d c dobson and c r vogel siam j numer anal 34 1997 pp 1779 1791 here we present a proof of the global and linear convergence using the framework introduced in h voss and u eckhart computing 25 1980 pp 243 251 and give a bound for the convergence rate of the fixed point iteration that agrees with our experimental results these results are also valid for suitable generalizations of the fixed point algorithm

large fluctuations of the macroscopic current in diffusive systems a numerical test of the additivity principle most systems when pushed out of equilibrium respond by building up currents of locally conserved observables understanding how microscopic dynamics determines the averages and fluctuations of these currents is one of the main open problems in nonequilibrium statistical physics the additivity principle is a theoretical proposal that allows to compute the current distribution in many one dimensional nonequilibrium systems using simulations we validate this conjecture in a simple and general model of energy transport both in the presence of a temperature gradient and in canonical equilibrium in particular we show that the current distribution displays a gaussian regime for small current fluctuations as prescribed by the central limit theorem and non gaussian exponential tails for large current deviations obeying in all cases the gallavotti cohen fluctuation theorem in order to facilitate a given current fluctuation the system adopts a well defined temperature profile different from that of the steady state and in accordance with the additivity hypothesis predictions system statistics during a large current fluctuation is independent of the sign of the current which implies that the optimal profile as well as higher order profiles and spatial correlations are invariant upon current inversion we also demonstrate that finite time joint fluctuations of the current and the profile are well described by the additivity functional these results suggest the additivity hypothesis as a general and powerful tool to compute current distributions in many nonequilibrium systems

current fluctuations in the one dimensional symmetric exclusion process with open boundaries we calculate the first four cumulants of the integrated current of the one dimensional symmetric simple exclusion process of n sites with open boundary conditions for large system size n the generating function of the integrated current depends on the densities a and b of the two reservoirs and on the fugacity z the parameter conjugated to the integrated current through a single parameter based on our expressions for these first four cumulants we make a conjecture which leads to a prediction for all the higher cumulants in the case a 1 and b 0 our conjecture gives the same universal distribution as the one obtained by lee levitov and yakovets for one dimensional quantum conductors in the metallic regime

universal distributions for growth processes in 1 1 dimensions and random matrices we develop a scaling theory for kardar parisi zhang growth in one dimension by a detailed study of the polynuclear growth model in particular we identify three universal distributions for shape fluctuations and their dependence on the macroscopic shape these distribution functions are computed using the partition function of gaussian random matrices in a cosine potential

stretched exponential decay in a kinetic ising model with dynamical constraint we show that for the standard nearest neighbor spin flip dynamics in one dimension with the constraint of constant energy the spin spin correlation function decays as exp c sqrt t for larget we prove an upper and lower bound the coefficientc of the lower bound is given as the solution of a variational problem and is conjectured to be exact

large deviation of the density profile in the steady state of the open symmetric simple exclusion process we consider an open one dimensional lattice gas on sites i 1 n with particles jumping independently with rate 1 to neighboring interior empty sites the simple symmetric exclusion process the particle fluxes at the left and right boundaries corresponding to exchanges with reservoirs at different chemical potentials create a stationary nonequilibrium state sns with a steady flux of particles through the system the mean density profile in this state which is linear describes the typical behavior of a macroscopic system i e this profile occurs with probability 1 when n the probability of microscopic configurations corresponding to some other profile x x i n has the asymptotic form exp n f f is the large deviation functional in contrast to equilibrium systems for which f eq is just the integral of the appropriately normalized local free energy density the f we find here for the nonequilibrium system is a nonlocal function of this gives rise to the long range correlations in the sns predicted by fluctuating hydrodynamics and suggests similar non local behavior of f in general sns where the long range correlations have been observed experimentally

fluctuations of current in nonstationary diffusive lattice gases we employ the macroscopic fluctuation theory to study fluctuations of integrated current in one dimensional lattice gases with a steplike initial density profile we analytically determine the variance of the current fluctuations for a class of diffusive processes with a density independent diffusion coefficient our calculations rely on a perturbation theory around the noiseless hydrodynamic solution we consider both quenched and annealed types of averaging the initial condition is allowed to fluctuate in the latter situation the general results for the variance are specialized to a few interesting models including the symmetric exclusion process and the kipnis marchioro presutti model kipnis marchioro and presutti j stat phys 27 65 1982 we also probe large deviations of the current for the symmetric exclusion process this is done by numerically solving the governing equations of the macroscopic fluctuation theory using an efficient iteration algorithm