A central limit theorem for Gibbs measures relative to Brownian motion

Volker Betz; Herbert Spohn

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A central limit theorem for Gibbs measures relative to Brownian motion

Volker Betz·Herbert Spohn

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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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Volker Betz, Herbert Spohn. 2003-08-20. A central limit theorem for Gibbs measures relative to Brownian motion. https://arxiv.org/abs/math/0308193

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