Hydrodynamics for the SSEP with non-reversible slow boundary dynamics: part I, the critical regime and beyond
Résumé
The purpose of this article is to provide a simple proof of the hydrodynamic and hydrostatic behavior of the SSEP in contact with slowed reservoirs which inject and remove particles in a finite size windows at the extremities of the bulk. More precisely, the reservoirs inject/remove particles at/from any point of a window of size K placed at each extremity of the bulk and particles are injected/removed to the first open/occupied position in that window. The hydrodynamic limit is given by the heat equation with non-linear Robin boundary conditions or Neumann boundary conditions, the latter being in the case when the reservoirs are too slow. The proof goes through the entropy method of [16]. We also derive the hydrostatic limit for this model, whose proof is based on the method developed in [18] and [20]. We observe that we do not make use of correlation estimates in none of our results.
Domaines
Probabilités [math.PR]Origine | Fichiers produits par l'(les) auteur(s) |
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