Work

Gibbs measures on Brownian currents

Year: 2007

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.0704.3237

Authors: Gubinelli, Massimiliano, Lorinczi, Jozsef

Institutions: Université Paris-Sud, Centre National de la Recherche Scientifique, Laboratoire de Mathématiques d'Orsay, Loughborough University, Technical University of Munich

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W2950105084

Cites: 26

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Related to: 20