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Stefan problem for a non-ergodic facilitated exclusion process

Oriane Blondel 1 Clément Erignoux 2 Marielle Simon 2
1 PSPM - Probabilités, statistique, physique mathématique
ICJ - Institut Camille Jordan [Villeurbanne]
2 Paradyse
LPP - Laboratoire Paul Painlevé - UMR 8524, Inria Lille - Nord Europe
Abstract : We consider the facilitated exclusion process, which is a non-ergodic, 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 non-trivial 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.
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https://hal.inria.fr/hal-02482922
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Submitted on : Monday, November 30, 2020 - 9:22:23 AM
Last modification on : Wednesday, November 17, 2021 - 11:27:22 AM

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Oriane Blondel, Clément Erignoux, Marielle Simon. Stefan problem for a non-ergodic facilitated exclusion process. Probability and Mathematical Physics, MSP, 2021, 2 (1), ⟨10.2140/pmp.2021.2.127⟩. ⟨hal-02482922v2⟩

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