Gibbs measures relative to Brownian motion

Hirofumi Osada, Herbert Spohn

Research output: Contribution to journalArticle

17 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)1183-1207
Number of pages25
JournalAnnals of Probability
Volume27
Issue number3
DOIs
Publication statusPublished - Jul 1999

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Fingerprint Dive into the research topics of 'Gibbs measures relative to Brownian motion'. Together they form a unique fingerprint.

  • Cite this