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arXiv · 2201.07097

Gaussian fluctuations of replica overlap in directed polymers

Yu Gu·Tomasz Komorowski
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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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Yu Gu, Tomasz Komorowski. 2022-01-18. Gaussian fluctuations of replica overlap in directed polymers. https://arxiv.org/abs/2201.07097

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