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

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 $d\ne 2$. 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.

35 pages, accepted for publication in Ann. Inst. H. Poincaré Probab. Statist

References in corpus (3)

• New characterization of the weak disorder phase of directed polymers in bounded random environments
• Law of large numbers and fluctuations in the sub-critical and $L^2$ regions for SHE and KPZ equation in dimension $d\ge 3$
• Edwards-Wilkinson fluctuations for the directed polymer in the full $L^2$-regime for dimensions $d\ge 3$