Paul Chleboun

University of Warwick

Mixing times for Facilitated Exclusion Processes

Probability Seminar

28th October 2022, 3:30 pm – 4:30 pm
Fry Building, 2.04

We consider facilitated exclusion processes (FEP) in one dimension. These models belong to a class of kinetically constrained lattice gases, the process was introduced in the physics literature motivated by studying the active-absorbing phase transition. Under the dynamics a particle can move to a neighbouring site provided that the target site is empty (the exclusion rule) and the other neighbour of the departure site is occupied (the constraint). These processes have recently attracted lot of attention due to their interesting hydrodynamic limit behaviour. We examine the mixing time, the time to reach equilibrium, on an interval with closed boundaries and also with periodic boundary conditions. On the interval we observe that asymmetry significantly changes the mixing behaviour. The analysis naturally splits into examining the time to reach the ergodic configurations (irreducible component) followed by the time needed to mix on this set of configurations. This is ongoing work with James Ayre (Oxford).

Organisers: Benjamin Lees, Jessica Jay

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