Existence of hydrodynamics for the totally asymmetric simple \(K\)-exclusion process
type: Item
instance of: scholarly article
title: Existence of hydrodynamics for the totally asymmetric simple \(K\)-exclusion process
zbMATH Open document ID: 0947.60088
author: Timo Seppäläinen
published in: The Annals of Probability
publication date: 1999-11-09T00:00:00Z
review text: The totally asymmetric simple \(K\)-exclusion process studied in the paper evolves as follows: Particles take nearest-neighbor steps to the right on the lattice \(\mathbb Z\), under the constraint that each site contains at most \(K\) partic1es. It is proved that such processes satisfy hydrodynamic limits under Euler scaling, and that the 1imit of the empirical particle profile is the entropy solution of a scalar conservation law with a concave flux function. The proof mainly uses a coupling with a growth model on the two-dimensional lattice and requires, but does not use the knowledge of the invariant measures of the process, which is not known indeed. The author treats the site-disordered case. This is still new, even for the simple exclusion process. The tools developed in the paper are rather interesting and may have other applications.
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 60K25
zbMATH DE Number: 1359649
zbMATH Keywords: \(K\)-exclusion process
zbMATH Keywords: marching soldiers model
zbMATH Keywords: hydrodynamic limit
reviewed by: Mu-Fa Chen
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1022677266
OpenAlex ID: W1596461964
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DOI: 10.1214/AOP/1022677266
description: scientific article; zbMATH DE number 1359649