Gaussian fluctuations of replica overlap in directed polymers
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}.
 Publication:

arXiv eprints
 Pub Date:
 January 2022
 arXiv:
 arXiv:2201.07097
 Bibcode:
 2022arXiv220107097G
 Keywords:

 Mathematics  Probability;
 Mathematical Physics
 EPrint:
 14 pages, v2 minor revisions