A Functional Central Limit Theorem for Polaron Path Measures

The application of the Feynman‐Kac formula to Polaron models of quantum theory leads to the path measure of Brownian motion perturbed by a pair potential that is translation invariant both in space and time. An important problem in this context is the validity of a central limit theorem in infinite volume. We show both the existence of the relevant infinite volume limits and a functional central limit theorem in a generality that includes the Fröhlich Polaron for all coupling constants. The proofs are based on an extension of a novel method by Mukherjee and Varadhan.