Symmetric exclusion process under stochastic power-law resetting

Distributional Limits for the Symmetric Exclusion Process

Strong negative dependence properties have recently been proved for the symmetric exclusion process. In this paper, we apply these results to prove convergence to the Poisson and Gaussian distributions for various functionals of the process.

Perturbations of the Symmetric Exclusion Process

One of the fundamental issues concerning particle systems is classifying the invariant measures I and giving properties of those measures for different processes. For the exclusion process with symmetric kernel p(x, y) = p(y, x), I has been completely studied. This paper gives results concerning I for exclusion processes where p(x, y) = p(y, x) except for finitely many x, y ∈ S and p(x, y) corr...

Diffusion with stochastic resetting.

We study simple diffusion where a particle stochastically resets to its initial position at a constant rate r. A finite resetting rate leads to a nonequilibrium stationary state with non-Gaussian fluctuations for the particle position. We also show that the mean time to find a stationary target by a diffusive searcher is finite and has a minimum value at an optimal resetting rate r*. Resetting ...

Symmetric Simple Exclusion Process: Regularity of the Self Diffusion Coefficient

Law of Large Numbers for the Asymmetric Simple Exclusion Process

We consider simple exclusion processes on Z for which the underlying random walk has a finite first moment and a non-zero mean and whose initial distributions are product measures with different densities to the left and to the right of the origin. We prove a strong law of large numbers for the number of particles present at time t in an interval growing linearly with t.