A functional central limit theorem for Polaron path measures
Probability
2021-06-14 v1 Mathematical Physics
math.MP
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.
Keywords
Cite
@article{arxiv.2106.06447,
title = {A functional central limit theorem for Polaron path measures},
author = {Volker Betz and Steffen Polzer},
journal= {arXiv preprint arXiv:2106.06447},
year = {2021}
}
Comments
39 pages, 2 figures