Gibbs measures on Brownian paths: Theory and applications
  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. 
Volker Betz, Jozsef Lorinczi and Herbert Spohn