Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

Stefan problem for a non-ergodic facilitated exclusion process

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.
Complete list of metadatas

Cited literature [35 references]  Display  Hide  Download

https://hal.inria.fr/hal-02482922
Contributor : Marielle Simon <>
Submitted on : Monday, April 6, 2020 - 3:50:16 PM
Last modification on : Monday, April 6, 2020 - 3:58:00 PM

File

Facilitated_ex_Free_Boundary.p...
Files produced by the author(s)

Identifiers

  • HAL Id : hal-02482922, version 1
  • ARXIV : 1912.09583

Citation

Oriane Blondel, Clément Erignoux, Marielle Simon. Stefan problem for a non-ergodic facilitated exclusion process. 2020. ⟨hal-02482922⟩

Share

Metrics

Record views

72

Files downloads

51