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arXiv · 2106.06447

A functional central limit theorem for Polaron path measures

Volker Betz·Steffen Polzer
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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.

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Volker Betz, Steffen Polzer. 2021-06-11. A functional central limit theorem for Polaron path measures. https://arxiv.org/abs/2106.06447

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