2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/57710We 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.27 pagesMathematical Physics82B31text