Vol. 2, No. 1, 2021

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Stefan problem for a nonergodic facilitated exclusion process

Oriane Blondel, Clément Erignoux and Marielle Simon

Vol. 2 (2021), No. 1, 127–178
Abstract

We consider the facilitated exclusion process, which is a nonergodic, kinetically constrained exclusion process. We show that in the hydrodynamic limit, its macroscopic behavior is governed by a free boundary problem. The particles evolve on the one-dimensional lattice according to jump rates which are degenerate, since they can vanish on nontrivial configurations and create distinct phases: indeed, configurations can be totally blocked (they cannot evolve under the dynamics), ergodic (they belong to an irreducible component), or transient (after a transitive period of time they will become either blocked or ergodic). We additionally prove that the microscopic separation into blocked/ergodic phases fully coincides with the moving interface problem given by the hydrodynamic equation.

Keywords
hydrodynamic limits, kinetically constrained exclusion process, active-absorbing phase transition, Stefan problem
Mathematical Subject Classification 2010
Primary: 35R35, 60J27, 60K35
Milestones
Received: 17 February 2020
Revised: 8 October 2020
Accepted: 27 October 2020
Published: 16 March 2021
Authors
Oriane Blondel
CNRS, UMR5208
Université Claude Bernard Lyon 1
Institut Camille Jordan
Villeurbanne Cedex
France
Clément Erignoux
CNRS, UMR 8524 Laboratoire Paul Painlevé
Inria, Univ. Lille
Villeneuve d’Ascq
France
Marielle Simon
CNRS, UMR 8524 Laboratoire Paul Painlevé
Inria, Univ. Lille
Villeneuve d’Ascq
France