Related papers: Exclusion processes with non-reversible boundary: …
We consider an interacting particle system in the interval $[1,N]$ with reservoirs at the boundaries. While the dynamics in the channel is the simple symmetric exclusion process, the reservoirs are also particle systems which interact with…
For reaction-diffusion processes without exclusion, in which the particles can exist in the same site of a one-dimensional lattice, we study all the integrable models which can be obtained by imposing a boundary condition on the master…
We consider the weakly asymmetric exclusion process on a bounded interval with particles reservoirs at the endpoints. The hydrodynamic limit for the empirical density, obtained in the diffusive scaling, is given by the viscous Burgers…
Asymmetric exclusion processes with locally reversible kinetic constraints are introduced to investigate the effect of non-conservative driving forces in athermal systems. At high density they generally exhibit rheological-like behavior,…
We study a totally asymmetric simple exclusion process where jumps happen at rate one, except at the origin where the rate is lower. We prove a hydrodynamic scaling limit to a macroscopic profile described by a variational formula. The…
Dynamical phase transitions are crucial features of the fluctuations of statistical systems, corresponding to boundaries between qualitatively different mechanisms of maintaining unlikely values of dynamical observables over long periods of…
Let $\Lambda$ be a connected closed region with smooth boundary contained in the $d$-dimensional continuous torus $\bb T^d$. In the discrete torus $N^{-1} \bb T^d_N$, we consider a nearest neighbor symmetric exclusion process where…
The behaviour of extended particles with exclusion interaction on a one-dimensional lattice is investigated. The basic model is called $\ell$-ASEP as a generalization of the asymmetric exclusion process (ASEP) to particles of arbitrary…
This study deals with continuous limits of interacting one-dimensional diffusive systems, arising from stochastic distortions of discrete curves with various kinds of coding representations. These systems are essentially of a…
This paper focuses on a drift-diffusion system subjected to boundedly non dissipative Robin boundary conditions. A general existence result with large initial conditions is established by using suitable L1, L2 and trace estimates. Finally,…
We obtain the large scale limit of the fluctuations around its hydrodynamic limit of the density of particles of a weakly asymmetric exclusion process in dimension up to three. The proof is based upon a sharp estimate on the relative…
Given a doubly infinite sequence of positive numbers {c_k: k in Z} satisfying a LLN with limit A, we consider the nearest-neighbor simple exclusion process on Z where c_k is the probability rate of jumps between k and k+1. If A is infinite…
The boundary conditions at the deformable interface between two contacting fluids are derived for the general case of the large-amplitude perturbations. The interface is modeled as perturbed free boundary that evolves in time, and the…
We study large deviations for the current of one-dimensional stochastic particle systems with periodic boundary conditions. Following a recent approach based on an earlier result by Jensen and Varadhan, we compare several candidates for…
A fractional Fick's law and fractional hydrostatics for the one dimensional exclusion process with long jumps in contact with infinite reservoirs at different densities on the left and on the right are derived.
We study the heat equation on a half-space with a linear dynamical boundary condition. Our main aim is to show that, if the diffusion coefficient tends to infinity, then the solutions converge (in a suitable sense) to solutions of the…
We consider a general class of nonlinear diffusive models with bulk dissipation and boundary driving, and derive its hydrodynamic description in the large size limit. Both the average macroscopic behavior and the fluctuating properties of…
By considering the master equation of asymmetric exclusion process on a one-dimensional lattice, we obtain the most general boundary condition of the multi-species exclusion processes in which the number of particles is constant in time.…
This work concerns generalized backward stochastic differential equations, which are coupled with a family of reflecting diffusion processes. First of all, we establish the large deviation principle for forward stochastic differential…
We investigate a boundary-driven Ginzburg-Landau dynamics with long-range interactions. In the hydrodynamic limit, the macroscopic evolution is governed by a fractional heat equation with Dirichlet boundary conditions, while the…