Gaussian fluctuations of replica overlap in directed polymers
Yu Gu, Tomasz Komorowski
TL;DR
This paper establishes a central limit theorem for replica overlap in Brownian directed polymers within Gaussian environments, utilizing superconcentration results for the KPZ equation, applicable across all dimensions and low temperatures.
Contribution
It introduces a novel CLT for replica overlap in directed polymers, connecting superconcentration of KPZ to polymer fluctuations, extending understanding in low-temperature regimes.
Findings
Proves a CLT for replica overlap in directed polymers
Demonstrates superconcentration for the KPZ equation with mollified noise
Applicable in all dimensions at low temperature
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}.
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Taxonomy
TopicsStochastic processes and statistical mechanics · Stochastic processes and financial applications · Random Matrices and Applications