Gaussian fluctuations of replica overlap in directed polymers
Probability
2022-06-29 v2 Mathematical Physics
math.MP
Abstract
In this short note, we prove a central limit theorem for a type of replica overlap of the Brownian directed polymer in a Gaussian random environment, in the low temperature regime and in all dimensions. The proof relies on a superconcentration result for the KPZ equation driven by a spatially mollified noise, which is inspired by the recent work of Chatterjee \cite{C1}.
Keywords
Cite
@article{arxiv.2201.07097,
title = {Gaussian fluctuations of replica overlap in directed polymers},
author = {Yu Gu and Tomasz Komorowski},
journal= {arXiv preprint arXiv:2201.07097},
year = {2022}
}
Comments
14 pages, v2 minor revisions