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Journal Articles Probability and Mathematical Physics Year : 2021

Stefan problem for a non-ergodic facilitated exclusion process

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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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Dates and versions

hal-02482922 , version 1 (06-04-2020)
hal-02482922 , version 2 (30-11-2020)

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