Gibbs measures on Brownian currents

Lorinczi, József; Gubinelli, Massimiliano

Lorinczi, József; Gubinelli, Massimiliano (2009), Gibbs measures on Brownian currents, Communications on Pure and Applied Mathematics, 62, 1, p. 1-56. http://dx.doi.org/10.1002/cpa.20260

Type

Article accepté pour publication ou publié

Date

2009

Journal name

Communications on Pure and Applied Mathematics

Volume

Number

Publisher

Wiley Periodicals, Inc.

Pages

1-56

Abstract (EN)

Motivated by applications to quantum field theory we consider Gibbs measures for which the reference measure is Wiener measure and the interaction is given by a double stochastic integral and a pinning external potential. In order properly to characterize these measures through DLR equations, we are led to lift Wiener measure and other objects to a space of configurations where the basic observables are not only the position of the particle at all times but also the work done by test vector fields. We prove existence and basic properties of such Gibbs measures in the small coupling regime by means of cluster expansion.

Subjects / Keywords

Mathematical Physics