Related papers: Stationary measure for the open KPZ equation

We focus on the three-state quantum walk(QW) in one dimension. In this paper, we give the stationary measure in general condition, originated from the eigenvalue problem. Firstly, we get the transfer matrices by our new recipe, and solve…

The Kardar-Parisi-Zhang (KPZ) universality class describes a large class of 2-dimensional models of random growth, which exhibit universal scaling exponents and limiting statistics. The last ten years has seen remarkable progress in this…

We find conditions for stationary measures of random dynamical systems on surfaces having dissipative diffeomorphisms to be absolutely continuous. These conditions involve a uniformly expanding on average property in the future (UEF) and…

Recent works of Barraquand and Le Doussal and Bryc, Kuznetsov, Wang, and Wesolowski gave a description of the open KPZ stationary measure as the sum of a Brownian motion and a Brownian motion reweighted by a Radon-Nikodym derivative.…

We demonstrate that Liggett's condition can be relaxed without disrupting the convergence of open ASEP stationary measures to the open KPZ stationary measure. This is equivalent to demonstrating that, under weak asymmetry scaling and…

We show that the stationary measure for the totally asymmetric simple exclusion process on a segment with open boundaries is given by a marginal of a two-line measure with a simple and explicit description. We use this representation to…

We consider the one dimensional boundary driven harmonic model and its continuous version, both introduced in \cite{FGK}. By combining duality and integrability the authors of \cite{FG} obtained the invariant measures in a combinatorial…

We investigate the unique stationary measure of a positive recurrent reflecting Brownian motion in the upper half-plane, where the direction of reflection is constant on each half-axis. The Laplace transform of the stationary distribution…

We give necessary and sufficient conditions for a multivariate stationary stochastic process to be completely regular. We also give the answer to a question of V.V. Peller concerning the spectral measure characterization of such processes.

We study the invariant measure of a discretized stochastic Allen-Cahn equation in d+1 dimensions in the low noise limit. We consider a cuboidal domain and impose the two stable phases as boundary conditions at two opposite faces. We then…

We study general zero range processes with different types of particles on a d-dimensional lattice with periodic boundary conditions. A necessary and sufficient condition on the jump rates for the existence of stationary product measures is…

The periodic KdV equation u_t=u_{xxx}+\beta uu_x arises from a Hamiltonian system with infinite-dimensional phase space L^2(T). Bourgain has shown that there exists a Gibbs measure \nu on balls \{\phi :\Vert\Phi\Vert^2_{L^2}\leq N\} in the…

We initiate the study of random iteration of automorphisms of real and complex projective surfaces, or more generally compact K{\"a}hler surfaces, focusing on the fundamental problem of classification of stationary measures. We show that,…

We study the problem of classifying stationary measures and orbit closures for non-abelian action on a surface with a given smooth invariant measure. Using a result of Brown and Rodriguez Hertz, we show that under a certain finite…

Current fluctuations for the one-dimensional totally asymmetric exclusion process (TASEP) connected to reservoirs of particles, and their large scale limit to the KPZ fixed point in finite volume, are studied using exact methods. Focusing…

This paper is concerned with $3$-D stochastic Euler-Poisson equations with insulating boundary conditions forced by the Wiener process. We first establish the global existence and uniqueness of the solution to the system, then we prove that…

We construct explicit jointly invariant measures for the periodic KPZ equation (and therefore also the stochastic Burgers' and stochastic heat equations) for general slope parameters and prove their uniqueness via a one force--one solution…

We study the stochastic six-vertex model on a strip $$\left\{(x,y)\in\mathbb{Z}^2: 0\leq y\leq x\leq y+N\right\}$$ with two open boundaries. We develop a `matrix product ansatz' method to solve for its stationary measure, based on the…

We consider a measurable stationary Gaussian stochastic process. A criterion for testing hypotheses about the covariance function of such a process using estimates for its norm in the space $L_p(\mathbb {T}),\,p\geq1$, is constructed.

We develop a volume penalization method for inhomogeneous Neumann boundary conditions, generalizing the flux-based volume penalization method for homogeneous Neumann boundary condition proposed by Kadoch et al. [J. Comput. Phys. 231 (2012)…