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We consider the symmetric exclusion process on the $d$-dimensional lattice with translational invariant and ergodic initial data. It is then known that as $t$ diverges the distribution of the process at time $t$ converges to a Bernoulli product measure. Assuming a summable decay of correlations of the initial data, we prove a quantitative version of this convergence by obtaining an explicit bound on the Ornstein $bar d$-distance. The proof is based on the analysis of a two species exclusion process with annihilation.
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 normal distributions for various functionals of the process.
We study mixing times of the symmetric and asymmetric simple exclusion process on the segment where particles are allowed to enter and exit at the endpoints. We consider different regimes depending on the entering and exiting rates as well as on the
We analyze the mixing behavior of the biased exclusion process on a path of length $n$ as the bias $beta_n$ tends to $0$ as $n to infty$. We show that the sequence of chains has a pre-cutoff, and interpolates between the unbiased exclusion and the pr
We consider the simple exclusion process on Z x {0, 1}, that is, an horizontal ladder composed of 2 lanes. Particles can jump according to a lane-dependent translation-invariant nearest neighbour jump kernel, i.e. horizontally along each lane, and ve
A fractional Ficks 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.