Self-diffusion for Brownian motions with local interaction

Ilie Grigorescu

doi:10.1214/aop/1022677445

Self-diffusion for Brownian motions with local interaction

Ilie Grigorescu

Research output: Contribution to journal › Article

7 Scopus citations

Abstract

We derive explicitly the asymptotic law of the tagged particle process in a system of interacting Brownian motions in the presence of a diffusive scaling in nonequilibrium. The interaction is local and interpolates between the totally independent case (noninteracting) and the totally reflecting case and can be viewed as the limiting local version of an interaction through a pair potential as its support shrinks to zero. We also prove the independence of two tagged particles in the limit.

Original language	English (US)
Pages (from-to)	1208-1267
Number of pages	60
Journal	Annals of Probability
Volume	27
Issue number	3
DOIs	https://doi.org/10.1214/aop/1022677445
State	Published - Jul 1999
Externally published	Yes

Keywords

Bounded initial density profile
Local time
Martingale problem
Tagged particle

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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Grigorescu, I. (1999). Self-diffusion for Brownian motions with local interaction. Annals of Probability, 27(3), 1208-1267. https://doi.org/10.1214/aop/1022677445

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AB - We derive explicitly the asymptotic law of the tagged particle process in a system of interacting Brownian motions in the presence of a diffusive scaling in nonequilibrium. The interaction is local and interpolates between the totally independent case (noninteracting) and the totally reflecting case and can be viewed as the limiting local version of an interaction through a pair potential as its support shrinks to zero. We also prove the independence of two tagged particles in the limit.

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KW - Martingale problem

KW - Tagged particle

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