Symmetric simple exclusion process with free boundaries

Anna De Masi, Pablo A. Ferrari, Errico Presutti

Published 2013-04-02, updated 2014-01-04Version 2

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.