Mixing time of the Asymmetric Zero Range process on the segment

15:50-16:10 Tuesday, 6 May 2025Auditorium, Rectorate

Abstract

In this talk, we shall discuss the mixing time of the Asymmetric Zero Range process (AZRP) with non-decreasing jump rates on the segment. We will first study the hydrodynamic limit starting from the configuration where all particles are gathered on the left-most site. The macroscopic equilibrium time gives a lower bound on the mixing time. We will show the sharpness of this estimate when the system is asymmetric enough, which establishes the cut-off phenomenon. This extends earlier results of Labbe and Lacoin in the context of the asymmetric simple exclusion process.