A variational coupling for a totally asymmetric exclusion process with long jumps but no passing

1999/06/28 by Timo Seppalainen
Mathematics · #math.PR #msc:60K35

paper · pdf

published as Hydrodynamic limits and related topics (Toronto, ON, 1998), 117-130, Fields Inst. Commun., 27, Amer. Math. Soc., Providence, RI, 2000 · Proceedings of the workshop on hydrodynamic limits, The Fields Institute, Toronto (October 1998)

arxiv created 1999/06/28 · arxiv updated 2009/11/30

Abstract

We prove a weak law of large numbers for a tagged particle in a totally asymmetric exclusion process on the one-dimensional lattice. The particles are allowed to take long jumps but not pass each other. The object of the paper is to illustrate a special technique for proving such theorems. The method uses a coupling that mimics the Hopf-Lax formula from the theory of viscosity solutions of Hamilton-Jacobi equations.

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