BETZ, V., LORINCZI, J. and SPOHN, H., Gibbs measures on Brownian paths: theory and applications. arXiv:math-ph/0404062
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.