Massimiliano Gubinelli and Jozsef Lorinczi
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.
Massimiliano Gubinelli and Jozsef Lorinczi. Gibbs measures on Brownian currents. Papers of Massimiliano Gubinelli, 2007, version 1. https://mgubi.org/papers/paper/gibbs-brownian-currents/
Pin in the collection (SHA-512 of the inventory it fixes):
85182a07beffd8efe5909efe31ab2368fe8ac4c57c6a1ff0c194f7c6340c437d88a71d31b08941b754bad1a4335f3965ae7823d974cec869932df9dd88ecb272
Papers of Massimiliano Gubinelli: an OpenSheaf archive (format 0.1, a draft); this page is generated by opensheaf-py from the archive.