Date
2009
Dewey
Probabilités et mathématiques appliquées
Sujet
Mathematical Physics
Journal issue
Communications on Pure and Applied Mathematics
Volume
62
Number
1
Publication date
2009
Article pages
1-56
Publisher
Wiley Periodicals, Inc.
Author
Lorinczi, József
Gubinelli, Massimiliano
Type
Article accepté pour publication ou publié
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.