Diffusion processes on path spaces with interactions

Yuu Hariya, Hirofumi Osada

研究成果: Contribution to journalArticle査読

1 被引用数 (Scopus)

抄録

We construct dynamics on path spaces C(ℝ;ℝ) and C([-r,r];ℝ) whose equilibrium states are Gibbs measures with free potential φ and interaction potential ψ. We do this by using the Dirichlet form theory under very mild conditions on the regularity of potentials. We take the carré du champ similar to the one of the Ornstein-Uhlenbeck process on C([0, ∞);ℝ). Our dynamics are non-Gaussian because we take Gibbs measures as reference measures. Typical examples of free potentials are double-well potentials and interaction potentials are convex functions. In this case the associated infinite-volume Gibbs measures are singular to any Gaussian measures on C(ℝ;ℝ).

本文言語英語
ページ(範囲)199-220
ページ数22
ジャーナルReviews in Mathematical Physics
13
2
DOI
出版ステータス出版済み - 2 1 2001
外部発表はい

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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