Mixing of the exclusion process with small bias

David A. Levin; Yuval Peres

doi:10.1007/s10955-016-1664-z

paper

Mixing of the exclusion process with small bias

arXiv:1608.03633 · doi:10.1007/s10955-016-1664-z

Abstract

We analyze the mixing behavior of the biased exclusion process on a path of length $n$ as the bias $β_{n}$ 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 process with constant bias. As the bias increases, the mixing time undergoes two phase transitions: one when $β_{n}$ is of order $1/ n$ , and the other when $β_{n}$ is order $lo g n / n$ .

15 pages, 4 figures