Mixing of the exclusion process with small bias

Abstract

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 process with constant bias. As the bias increases, the mixing time undergoes two phase transitions: one when ${\beta }_n$ is of order $1/n$, and the other when ${\beta }_n$ is order $\log n/n$.

15 pages, 4 figures

References in corpus (2)

• Mixing times of lozenge tiling and card shuffling Markov chains
• Mixing time and cutoff for the adjacent transposition shuffle and the simple exclusion

Cited by in corpus (4)

• Cutoff phenomenon for the asymmetric simple exclusion process and the biased card shuffling
• Mixing times for the simple exclusion process in ballistic random environment
• Sampling Biased Monotonic Surfaces using Exponential Metrics
• Mixing time for the asymmetric simple exclusion process in a random environment