Approach to equilibrium for Markovian infinite particle systems with exclusion interaction

Persistent Link:
http://hdl.handle.net/10150/282248
Title:
Approach to equilibrium for Markovian infinite particle systems with exclusion interaction
Author:
Keisling, John Davis, 1969-
Issue Date:
1996
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
The N-exclusion process is an interacting particle system that generalizes the simple exclusion process by allowing up to N particles at each site. In this work, we define the jump rates to be 1 if any particles are present and 0 if not, and we consider the infinite-volume limit of this process in arbitrary dimension. Assuming symmetry and translation invariance of the underlying Markov chain, we show that the extremal translation-invariant stationary measures are product measures, one for each given "density" of particles. With the further assumption of irreducibility, we generalize a coupling argument of Liggett to show that every translation-invariant measure converges to a mixture of these product measures.
Type:
text; Dissertation-Reproduction (electronic)
Keywords:
Mathematics.
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Graduate College; Mathematics
Degree Grantor:
University of Arizona
Advisor:
Faris, William G.

Full metadata record

DC FieldValue Language
dc.language.isoen_USen_US
dc.titleApproach to equilibrium for Markovian infinite particle systems with exclusion interactionen_US
dc.creatorKeisling, John Davis, 1969-en_US
dc.contributor.authorKeisling, John Davis, 1969-en_US
dc.date.issued1996en_US
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.description.abstractThe N-exclusion process is an interacting particle system that generalizes the simple exclusion process by allowing up to N particles at each site. In this work, we define the jump rates to be 1 if any particles are present and 0 if not, and we consider the infinite-volume limit of this process in arbitrary dimension. Assuming symmetry and translation invariance of the underlying Markov chain, we show that the extremal translation-invariant stationary measures are product measures, one for each given "density" of particles. With the further assumption of irreducibility, we generalize a coupling argument of Liggett to show that every translation-invariant measure converges to a mixture of these product measures.en_US
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
dc.subjectMathematics.en_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.disciplineMathematicsen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorFaris, William G.en_US
dc.identifier.proquest9720649en_US
dc.identifier.bibrecord.b34568116en_US
All Items in UA Campus Repository are protected by copyright, with all rights reserved, unless otherwise indicated.