A central limit theorem for Gibbs measures relative to Brownian motion

2003/08/20 by Volker Betz, Herbert Spohn, Betz, Volker +1
Mathematics · Physics and Astronomy · #60F17 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #math-ph #math.MP #math.PR #msc:60F17

paper · pdf · doi:10.48550/arxiv.math/0308193

19 pages

arxiv created 2003/08/20 · arxiv updated 2009/12/01

Abstract

We study a Gibbs measure over Brownian motion with a pair potential which depends only on the increments. Assuming a particular form of this pair potential, we establish that in the infinite volume limit the Gibbs measure can be viewed as Brownian motion moving in a dynamic random environment. Thereby we are in a position to use the technique of Kipnis and Varadhan and to prove a functional central limit theorem.

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