A central limit theorem for Gibbs measures relative to Brownian motion

✍ Scribed by Volker Betz; Herbert Spohn

• Publisher: Springer
• Year: 2004
• Tongue: English
• Weight: 230 KB
• Volume: 131
• Category: Article
• ISSN: 1432-2064
• DOI: 10.1007/s00440-004-0381-8

✦ Synopsis

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.