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July 1999 Gibbs Measures Relative to Brownian Motion
Hirofumi Osada, Herbert Spohn
Ann. Probab. 27(3): 1183-1207 (July 1999). DOI: 10.1214/aop/1022677444


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.


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Hirofumi Osada. Herbert Spohn. "Gibbs Measures Relative to Brownian Motion." Ann. Probab. 27 (3) 1183 - 1207, July 1999.


Published: July 1999
First available in Project Euclid: 29 May 2002

zbMATH: 0965.60095
MathSciNet: MR1733145
Digital Object Identifier: 10.1214/aop/1022677444

Primary: 60K35 , 82B21

Keywords: Brownian motion , Gibbs measure , pair potential

Rights: Copyright © 1999 Institute of Mathematical Statistics

Vol.27 • No. 3 • July 1999
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