Title :

Hydrodynamics for the SSEP with non-reversible slow boundary dynamics: part I, the critical regime and beyond

Author(s) :

Erignoux, Clement [Auteur]
Systèmes de particules et systèmes dynamiques [Paradyse]
Gonçalves, P [Auteur]
Nahum, G [Auteur]

Journal title :

Journal of Statistical Physics

Pages :

1433--1469

Publisher :

Springer Verlag

Publication date :

2020-09-18

ISSN :

0022-4715

HAL domain(s) :

Mathématiques [math]/Probabilités [math.PR]

English abstract : [en]

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 ...
Show more >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.Show less >

Language :

Anglais

Popular science :

Non

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL