Abstract not found

Abstract. µ being a nonnegative measure satisfying some Log-Sobolev inequality, we give conditions on F for the Boltzmann measure ν = e −2F µ to also satisfy some Log-Sobolev inequality. This paper improves and completes the final section in [6]. A general sufficient condition and a general necessary condition are given and examples are explicitly studied. Résumé. µ étant une mesure positive satisfaisant une inégalité de Sobolev logarithmique, nous donnons des conditions sur F pour que la mesure de Boltzmann ν = e −2F µ satisfasse également une telle inégalité (améliorant et complétant ainsi la dernière partie de [6]). Les conditions obtenues sont illustrées par des exemples.

We prove in this paper an existence result for in nite-dimensional stationary weakly interactive Brownian diusions. The interaction is very general in the sense that it is not supposed to be regular, and it also could be non-Markovian, but it is small enough. Our method consists in using the characterization of such diusions as space-time Gibbs elds so that we construct them by space-time cluster expansions in the small coupling parameter.

Abstract. Let (Bt; t ≥ 0) be a one- dimensional Brownian motion, with local time process (Lx t; t ≥ 0, x ∈ R). We determine the rate of decay of Z V [ { t (x): = Ex exp − 1 L

one-dimensional diffusions and integrability of hitting