Gibbs measures for self-interacting Wiener paths

M. Gubinelli

First issued 22 November 2005 · PDF

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 $\sigma$-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.

Versions

1. Version 2 (arXiv v2) current
   7 March 2006
   arXiv comments: 15 pages, no figures; typos, details added to the proofs
   PDF · LaTeX source · files and digests · arXiv:math-ph/0511068
2. Version 1 (arXiv v1)
   22 November 2005
   arXiv comments: 15 pages, no figures
   PDF · LaTeX source · files and digests · arXiv:math-ph/0511068

Cite

M. Gubinelli. Gibbs measures for self-interacting Wiener paths. Papers of Massimiliano Gubinelli, 2005, version 2. https://mgubi.org/papers/paper/self-interacting-wiener-paths/

Licence: arXiv.org non-exclusive license to distribute, assumed for submissions of 1991-2003; all other rights reserved to the authors

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