Perturbation of the equilibrium for a totally asymmetric stick process in one dimension

Simple item page
dc.creatorSeppalainen, Timo
dc.date1999-09-02
dc.date.accessioned2026-07-07T05:30:37Z
dc.date.available2026-07-07T05:30:37Z
dc.descriptionWe study the evolution of a small perturbation of the equilibrium of a totally asymmetric one-dimensional interacting system. The model we take as example is Hammersley's process as seen from a tagged particle, which can be viewed as a process of interacting positive-valued stick heights on the sites of Z. It is known that under Euler scaling (space and time scale n) the empirical stick profile obeys the Burgers equation. We refine this result in two ways: If the process starts close enough to equilibrium, then over times n^νfor 1\leν<3, and up to errors that vanish in hydrodynamic scale, the dynamics merely translates the initial stick configuration. A time evolution for the perturbation is visible under a particular family of scalings: over times n^ν, 1<ν<3/2, a perturbation of order n^(1-ν) from equilibrium follows the inviscid Burgers equation. The results for the stick model are derived from asymptotic results for tagged particles in Hammersley's process.
dc.identifierhttps://arxiv.org/abs/math/9909011
dc.identifierhttp://arxiv.org/abs/math/9909011
dc.identifierAnn. Probab. 29 (2001), 176-204
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/79046
dc.subjectProbability
dc.subjectMathematical Physics
dc.subject60K35; 82C22
dc.titlePerturbation of the equilibrium for a totally asymmetric stick process in one dimension
dc.typetext

Files

Collections

arXiv