Open Access
2022 Gaussian fluctuations of replica overlap in directed polymers
Yu Gu, Tomasz Komorowski
Author Affiliations +
Electron. Commun. Probab. 27: 1-12 (2022). DOI: 10.1214/22-ECP476


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 [14].

Funding Statement

Y.G. was partially supported by the NSF through DMS-2203007/2203014. T.K. acknowledges the support of NCN grant 2020/37/B/ST1/00426.


We thank Erik Bates and Sourav Chatterjee for comments on the draft and two anonymous referees for a careful reading of the paper which helped to improve the presentation.


Download Citation

Yu Gu. Tomasz Komorowski. "Gaussian fluctuations of replica overlap in directed polymers." Electron. Commun. Probab. 27 1 - 12, 2022.


Received: 18 January 2022; Accepted: 27 June 2022; Published: 2022
First available in Project Euclid: 19 July 2022

MathSciNet: MR4368695
zbMATH: 1507.60138
Digital Object Identifier: 10.1214/22-ECP476

Primary: 60H07 , 60H15 , 82D60

Keywords: Directed polymer , KPZ equation , superconcentration

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