The Annals of Probability

Gibbs Measures Relative to Brownian Motion

Hirofumi Osada and Herbert Spohn

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Abstract

We consider Brownian motion perturbed by the exponential of an action. The action is the sum of an external, one-body potential and a two-body interaction potential which depends only on the increments. Under suitable conditions on these potentials, we establish existence and uniqueness of the corresponding Gibbs measure. We also provide an example where uniqueness fails because of a slow decay in the interaction potential.

Article information

Source
Ann. Probab., Volume 27, Number 3 (1999), 1183-1207.

Dates
First available in Project Euclid: 29 May 2002

Permanent link to this document
https://projecteuclid.org/euclid.aop/1022677444

Digital Object Identifier
doi:10.1214/aop/1022677444

Mathematical Reviews number (MathSciNet)
MR1733145

Zentralblatt MATH identifier
0965.60095

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 82B21

Keywords
Gibbs measure Brownian motion pair potential

Citation

Osada, Hirofumi; Spohn, Herbert. Gibbs Measures Relative to Brownian Motion. Ann. Probab. 27 (1999), no. 3, 1183--1207. doi:10.1214/aop/1022677444. https://projecteuclid.org/euclid.aop/1022677444


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