相关论文: Matching Large Deviation Bounds of the Zero-Range …

We consider an asymmetric zero range process in infinite volume with zero mean and random jump rates starting from equilibrium. We investigate the large deviations from the hydrodynamical limit of the empirical distribution of particles and…

We survey our recent articles dealing with one dimensional attractive zero range processes moving under site disorder. We suppose that the underlying random walks are biased to the right and so hyperbolic scaling is expected. Under the…

We study asymmetric zero-range processes on Z with nearest-neighbour jumps and site disorder. The jump rate of particles is an arbitrary but bounded nondecreasing function of the number of particles. For any given environment satisfying…

We consider a class of generalized long-range exclusion processes evolving either on $\mathbb Z$ or on a finite lattice with an open boundary. The jump rates are given in terms of a general kernel depending on both the departure and…

Large deviations of conservative interacting particle systems, such as the zero range process, about their hydrodynamic limit and their respective rate functions lead to the analysis of the skeleton equation; a degenerate…

This paper summarizes results and some open problems about the large-scale and long-time behavior of asymmetric, disordered exclusion and zero-range processes. These processes have randomly chosen jump rates at the sites of the underlying…

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…

We prove a large-deviation principle (LDP) for the sample paths of jump Markov processes in the small noise limit when, possibly, all the jump rates vanish uniformly, but slowly enough, in a region of the state space. We further discuss the…

We consider some interacting particle processes with long-range dynamics: the zero-range and exclusion processes with long jumps. We prove that the hydrodynamic limit of these processes corresponds to a (possibly non-linear) fractional heat…

In this article, we investigate the condensation phenomena for a class of nonreversible zero-range processes on a fixed finite set. By establishing a novel inequality bounding the capacity between two sets, and by developing a robust…

Two-species condensing zero range processes (ZRPs) are interacting particle systems with two species of particles and zero range interaction exhibiting phase separation outside a domain of sub-critical densities. We prove the hydrodynamic…

We study asymmetric zero-range processes on Z with nearest-neighbour jumps and site disorder. The jump rate of particles is an arbitrary but bounded nondecreasing function of the number of particles. We prove quenched strong local…

We consider a zero-range process $\eta^N_t(x)$ with superlinear local jump rate, which in a hydrodynamic-small particle rescaling converges to the porous medium equation $\partial_t u=\frac12\Delta u^\alpha, \alpha>1$. As a main result we…

We study the hydrodynamic behaviour of the symmetric zero-range process on the finite interval $\{1, \ldots, N-1\}$ in contact with slow reservoirs at the boundary. Particles are injected and removed at sites $1$ and $N-1$ at rates that…

We obtain a exponential large deviation upper bound for continuous observables on suspension semiflows over a non-uniformly expanding base transformation with non-flat singularities or criticalities, where the roof function defining the…

We study the exponential decay of relative entropy functionals for zero-range processes on the complete graph. For the standard model with rates increasing at infinity we prove entropy dissipation estimates, uniformly over the number of…

We study a zero-range process with system-size dependent jump rates, which is known to exhibit a discontinuous condensation transition. Metastable homogeneous phases and condensed phases coexist in extended phase regions around the…

We study large deviations for some non-local parabolic type equations. We show that, under some assumptions on the non-local term, problems defined in a bounded domain converge with an exponential rate to the solution of the problem defined…

We study lower large deviations for the current of totally asymmetric zero-range processes on a ring with concave current-density relation. We use an approach by Jensen and Varadhan which has previously been applied to exclusion processes,…

Using a weak convergence approach, we establish a Large Deviation Principle (LDP) for the solutions of fluid dynamic systems in two-dimensional bounded domains subjected to no-slip boundary conditions and perturbed by additive noise. Our…