Gaussian fluctuations of replica overlap in directed polymers

2022/01/18 by Yu Gu, Gu, Yu, Tomasz Komorowski +1
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2201.07097

openalex publication_date 2022/01/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 \citeC1.

Related

• Gaussian fluctuations for the directed polymer partition function for d≥ 3 and in the whole L²-region
• Free energy fluctuations for directed polymers in random media in 1+1 dimension
• Scaling properties of (2+1) directed polymers in the low temperature limit
• Directed polymers in random environment with heavy tails
• A central limit theorem for two-dimensional directed polymers with critical spatial correlation