Diffusion processes on path spaces with interactions

Yuu Hariya, Hirofumi Osada

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


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).

Original languageEnglish
Pages (from-to)199-220
Number of pages22
JournalReviews in Mathematical Physics
Issue number2
Publication statusPublished - 2001 Feb


  • Dirichlet forms
  • Gibbs
  • Path valued diffusion


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