Sharp convergence to equilibrium for the SSEP with reservoirs
Coauthors: Patrícia Gonçalves, Milton Jara and Otávio Menezes We consider the symmetric simple exclusion process evolving on the interval of length n-1 in contact with reservoirs of density rho in (0,1) at the boundary. We use Yau's relative entropy method to show that if the initial measure is associated with a profile u_0 : [0,1] -> (0,1), then at explicit times t^n(b) that depend on u_0, the distance to equilibrium, in total variation distance, converges, as n -> infty, to a profile G(\gamma e^{-b}). The parameter \gamma also depends on the initial profile u_0 and G(m) stands for the total variation distance \| N(m,1) - N(0,1)\|_{TV}. |