A functional central limit theorem for Polaron path measures

TL;DR

This paper proves a functional central limit theorem for Polaron path measures, demonstrating the existence of infinite volume limits and extending the results to all coupling constants using advanced probabilistic methods.

Contribution

It establishes the validity of a functional central limit theorem for Polaron models, including the Fröhlich polaron, for all coupling strengths, using an extension of Mukherjee and Varadhan's method.

Findings

Proves the existence of infinite volume limits for Polaron path measures.

Establishes a functional central limit theorem for these measures.

Extends results to all coupling constants in the Fröhlich polaron model.

Abstract

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 Fr\"ohlich polaron for all coupling constants. The proofs are based on an extension of a novel method by Mukherjee and Varadhan.