Asymptotic Behavior of a Tagged Particle in Simple Exclusion Processes

Nonequilibrium Fluctuations for a Tagged Particle in Mean-zero One-dimensional Zero-range Processes

We prove a non-equilibrium functional central limit theorem for the position of a tagged particle in mean-zero one-dimensional zero-range process. The asymptotic behavior of the tagged particle is described by a stochastic differential equation governed by the solution of the hydrodynamic equation.

Poissonian Approximation for the Tagged Particle in Asymmetric Simple Exclusion

We consider the position of a tagged particle in the one-dimensional asymmetric nearest-neighbor simple exclusion process. Each particle attempts to jump to the site to its right at rate p and to the site to its left at rate q. The jump is realized if the destination site is empty. We assume p > q. The initial distribution is the product measure with density 2, conditioned to have a particle at...

Asymptotic Behavior of Multivariate Reward Processes with Nonlinear Reward Functions

Diffusive variance for a tagged particle in d ≤ 2 asymmetric simple exclusion

The study of equilibrium fluctuations of a tagged particle in finite-range simple exclusion processes has a long history. The belief is that the scaled centered tagged particle motion behaves as some sort of homogenized random walk. In fact, invariance principles have been proved in all dimensions d ≥ 1 when the single particle jump rate is unbiased, in d ≥ 3 when the jump rate is biased, and i...

Asymmetric conservative processes with random rates

We study a one-dimensional nearest neighbor simple exclusion process for which the rates of jump are chosen randomly at time zero and fixed for the rest of the evolution. The ith particle's right and left jump rates are denoted pi and qi respectively; pi + qi 1. We fix c E (1/2, 1) and assume that pi E [c, 1] is a stationary ergodic process. We show that there exists a critical density p* depen...