Symmetric simple exclusion process with free boundaries

Abstract

We consider the one dimensional symmetric simple exclusion process (SSEP) with additional births and deaths restricted to a subset of configurations where there is a leftmost hole and a rightmost particle. At a fixed rate birth of particles occur at the position of the leftmost hole and at the same rate, independently, the rightmost particle dies. We prove convergence to a hydrodynamic limit and discuss its relation with a free boundary problem.

29 pages, 4 figures

References in corpus (2)

• The scaling limit of polymer pinning dynamics and a one dimensional Stefan freezing problem
• Hydrodynamic limit in a particle system with topological interactions

Cited by in corpus (3)

• Super-hydrodynamic limit in interacting particle systems
• The scaling limit of polymer pinning dynamics and a one dimensional Stefan freezing problem
• Hydrodynamic limit in a particle system with topological interactions