Mixing of the Exclusion Process with Small Bias

摘要

We analyze the mixing behavior of the biased exclusion process on a path of length n as the bias tends to 0 as . 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 is of order 1 / n, and the other when is order .