MIXING TIMES FOR THE SIMPLE EXCLUSION PROCESS WITH OPEN BOUNDARIES

Nina Gantert, Evita Nestoridi, Dominik Schmid

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

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 rates in the bulk, and show that the process exhibits pre-cutoff and in some cases cutoff. Our main contribution is to study mixing times for the asymmetric simple exclusion process with open boundaries. We show that the order of the mixing time can be linear or exponential in the size of the segment depending on the choice of the boundary parameters, proving a strikingly different (and richer) behavior for the simple exclusion process with open boundaries than for the process on the closed segment. Our arguments combine coupling, second class particle and censoring techniques with current estimates. A novel idea is the use of multi-species particle arguments, where the particles only obey a partial ordering.

Original languageEnglish (US)
Pages (from-to)972-1012
Number of pages41
JournalAnnals of Applied Probability
Volume33
Issue number2
DOIs
StatePublished - Apr 2023

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Keywords

  • Exclusion process
  • coupling
  • mixing times
  • second class particles

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