Sharp convergence to stationarity
for the SSEP on the square grid with reservoirs Coauthors: Milton Jara We consider the symmetric simple exclusion process evolving on the square grid of length n-1 in contact with boundary reservoirs of density rho in (0,1) and whose initial measure is associated with a profile u_0:[0,1]² -> (0,1). We extend the ideas of (GJMM, 2021) to dimension two, proving that the distance to equilibrium, in total variation, converges to a profile, in the following sense: there is an explicit positive real function t^n, which depends on u_0, such that the distance to equilibrium at time t^n(b) converges, as n inscreases, to G(\gamma e^{-b}), where \gamma also depends on the initial profile u_0 and G(m) := \| N (m,1) - N(0,1)\|_{TV}. |