(1) Institut für Biomathematik and Biometrie, GSF Forschungszentrum, Postfach 1129, 85758 Neuherberg, Germany;(2) Zentrum Mathematik, Technische Universität München, Boltzmannstr. 3, 85747 Garching, Germany
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.