Central limit theorems for the (2+1)-dimensional directed polymer in the weak disorder limit

2021/04/15 by Simon Gabriel, Gabriel, Simon
Mathematics · #60F17 #60K37 #82B44 #82D60 #FOS: Mathematics #FOS: Physical sciences #Markov Chains and Monte Carlo Methods #Mathematical Dynamics and Fractals #Mathematical Physics (math-ph) #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · doi:10.48550/arxiv.2104.07755

openalex publication_date 2021/04/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, we present an invariance principle for the paths of the directed random polymer in space dimension two in the subcritical intermediate disorder regime. More precisely, the distribution of diffusively rescaled polymer paths converges in probability to the law of Brownian motion when taking the weak disorder limit. So far analogous results have only been established for d≠ 2. Along the way, we prove a local limit theorem which allows us to factorise the point-to-point partition function of the directed polymer into a product of two point-to-plane partition functions.

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