Gibbs measures on Brownian currents
Massimiliano Gubinelli, József Lörinczi
Source abstract
Abstract 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 to properly characterize these measures through Dobrushin‐Lanford‐Ruelle (DLR) equations, we are led to lifting 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 weak coupling regime by means of cluster expansion. © 2008 Wiley Periodicals, Inc.
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