Massimiliano Gubinelli and Jozsef Lorinczi
Gibbs measures on Brownian currents
(726K, postscript)

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 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.