Gibbs measures on Brownian paths: Theory and applications
Volker Betz, Jozsef Lorinczi, Herbert Spohn
Abstract
We review our investigations on Gibbs measures relative to Brownian motion, in particular the existence of such measures and their path properties, uniqueness, resp. non-uniqueness. For the case when the energy only depends on increments, we present a functional central limit theorem. We also explain connections with other work and state open problems of interest.
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