Hydrodynamic limit for two-species exclusion processes

Makiko Sasada

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

We consider two-species exclusion processes on the d-dimensional discrete torus taking the effects of exchange, creation and annihilation into account. The model is, in general, of nongradient type. We prove that the (charged) particle density converges to the solution of a certain nonlinear diffusion equation under a diffusive rescaling in space and time. We also prove a lower bound on the spectral gap for the generator of the process confined in a finite volume.

Original languageEnglish
Pages (from-to)494-521
Number of pages28
JournalStochastic Processes and their Applications
Volume120
Issue number4
DOIs
Publication statusPublished - 2010 Apr

Fingerprint

Exclusion Process
Hydrodynamic Limit
Nonlinear Diffusion Equation
Spectral Gap
Rescaling
Charged particles
Annihilation
Finite Volume
Torus
Hydrodynamics
Generator
Lower bound
Converge
Model

Keywords

  • Hydrodynamic limit
  • Interacting particle systems
  • Two-species exclusion processes

ASJC Scopus subject areas

  • Modelling and Simulation
  • Statistics and Probability
  • Applied Mathematics

Cite this

Hydrodynamic limit for two-species exclusion processes. / Sasada, Makiko.

In: Stochastic Processes and their Applications, Vol. 120, No. 4, 04.2010, p. 494-521.

Research output: Contribution to journalArticle

@article{90d3c00f1619444abe7c222eca16f3a3,
title = "Hydrodynamic limit for two-species exclusion processes",
abstract = "We consider two-species exclusion processes on the d-dimensional discrete torus taking the effects of exchange, creation and annihilation into account. The model is, in general, of nongradient type. We prove that the (charged) particle density converges to the solution of a certain nonlinear diffusion equation under a diffusive rescaling in space and time. We also prove a lower bound on the spectral gap for the generator of the process confined in a finite volume.",
keywords = "Hydrodynamic limit, Interacting particle systems, Two-species exclusion processes",
author = "Makiko Sasada",
year = "2010",
month = "4",
doi = "10.1016/j.spa.2010.01.002",
language = "English",
volume = "120",
pages = "494--521",
journal = "Stochastic Processes and their Applications",
issn = "0304-4149",
publisher = "Elsevier",
number = "4",

}

TY - JOUR

T1 - Hydrodynamic limit for two-species exclusion processes

AU - Sasada, Makiko

PY - 2010/4

Y1 - 2010/4

N2 - We consider two-species exclusion processes on the d-dimensional discrete torus taking the effects of exchange, creation and annihilation into account. The model is, in general, of nongradient type. We prove that the (charged) particle density converges to the solution of a certain nonlinear diffusion equation under a diffusive rescaling in space and time. We also prove a lower bound on the spectral gap for the generator of the process confined in a finite volume.

AB - We consider two-species exclusion processes on the d-dimensional discrete torus taking the effects of exchange, creation and annihilation into account. The model is, in general, of nongradient type. We prove that the (charged) particle density converges to the solution of a certain nonlinear diffusion equation under a diffusive rescaling in space and time. We also prove a lower bound on the spectral gap for the generator of the process confined in a finite volume.

KW - Hydrodynamic limit

KW - Interacting particle systems

KW - Two-species exclusion processes

UR - http://www.scopus.com/inward/record.url?scp=76349110760&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=76349110760&partnerID=8YFLogxK

U2 - 10.1016/j.spa.2010.01.002

DO - 10.1016/j.spa.2010.01.002

M3 - Article

AN - SCOPUS:76349110760

VL - 120

SP - 494

EP - 521

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

SN - 0304-4149

IS - 4

ER -