Gibbs Measures for Self-interacting Wiener Paths

Abstract

In this note we study a class of specifications over d-dimensional Wiener measure which are invariant under uniform translation of the paths. This degeneracy is removed by restricting the measure to the σ-algebra generated by the increments of the coordinate process. We address the problem of existence and uniqueness of Gibbs measures and prove a central limit theorem for the rescaled increments. These results apply to the study of the ground state of the Nelson model of a quantum particle interacting with a scalar boson field.

Cite this paper

@inproceedings{Gubinelli2008GibbsMF, title={Gibbs Measures for Self-interacting Wiener Paths}, author={Massimiliano Gubinelli}, year={2008} }