Gibbs measures relative to Brownian motion

Hirofumi Osada, Herbert Spohn

Research output: Contribution to journalArticle

16 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
Publication statusPublished - Jul 1 1999
Externally publishedYes

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Gibbs Measure
Brownian motion
Interaction
Increment
Existence and Uniqueness
Uniqueness
Decay

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

Gibbs measures relative to Brownian motion. / Osada, Hirofumi; Spohn, Herbert.

In: Annals of Probability, Vol. 27, No. 3, 01.07.1999, p. 1183-1207.

Research output: Contribution to journalArticle

Osada, H & Spohn, H 1999, 'Gibbs measures relative to Brownian motion', Annals of Probability, vol. 27, no. 3, pp. 1183-1207.
Osada, Hirofumi ; Spohn, Herbert. / Gibbs measures relative to Brownian motion. In: Annals of Probability. 1999 ; Vol. 27, No. 3. pp. 1183-1207.
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