2000/03/08 by Timo Seppalainen
Mathematics · Physics and Astronomy · #math.PR #math-ph #math.MP #msc:60K35 #msc:82C22
published as J. Statist. Phys. 102 (2001), 69-96
arxiv created 2000/03/08 · arxiv updated 2009/11/30
We study a totally asymmetric simple exclusion process where jumps happen at rate one, except at the origin where the rate is lower. We prove a hydrodynamic scaling limit to a macroscopic profile described by a variational formula. The limit is valid for all values of the slow rate. The only assumption required is that a law of large numbers holds for the initial particle distribution. This includes also deterministic initial configurations. The hydrodynamic description contains as an unknown parameter the macroscopic rate at the origin, which is strictly larger than the microscopic slow rate. The limit is proved by the variational coupling method.