Gibbs measures for self-interacting Wiener paths

2005/11/22 by Massimiliano Gubinelli, M. Gubinelli, Gubinelli, M. · 1 citation
Mathematics · Physics and Astronomy · #82B21 #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Mechanics and Applications #advanced mathematical theories #math-ph #math.MP #msc:82B21

paper · pdf · doi:10.48550/arxiv.math-ph/0511068

15 pages, no figures; typos, details added to the proofs

openalex publication_date 2005/11/22 · arxiv created 2006/03/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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• Non-Uniqueness of Gibbs measures relative to Brownian motion

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