A variational approach to Gibbs measures on function spaces

Abstract

We study develop a variational technique to study models from constructive quantum field theory. Our starting point is the interpretation of the Polchinski equation as the Hamilton-Jacobi-Bellman equation of a stochastic control problem. Using this technique we are able to show ultraviolet stability for certain models as well as decay of correlations and derive a large deviations principle in the semi-classical limit.