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.
CITATION STYLE
Betz, V., Lőrinczi, J., & Spohn, H. (2005). Gibbs Measures on Brownian Paths: Theory and Applications. In Interacting Stochastic Systems (pp. 75–102). Springer-Verlag. https://doi.org/10.1007/3-540-27110-4_5
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