Quasi-critical fluctuations for 2d directed polymers

TL;DR

This paper investigates the 2d directed polymer in a new quasi-critical regime, demonstrating Gaussian fluctuations and extending results to the critical stochastic heat flow, with novel moment estimates overcoming key challenges.

Contribution

It introduces a quasi-critical regime for 2d directed polymers and proves Gaussian fluctuations, bridging sub-critical and critical behaviors with new analytical techniques.

Findings

Gaussian fluctuations in quasi-critical regime

Asymptotic normality of partition functions

Extension to critical 2d Stochastic Heat Flow

Abstract

We study the 2d directed polymer in random environment in a novel *quasi-critical regime*, which interpolates between the much studied sub-critical and critical regimes. We prove Edwards-Wilkinson fluctuations throughout the quasi-critical regime, showing that the diffusively rescaled partition functions are asymptotically Gaussian. We deduce a corresponding result for the critical 2d Stochastic Heat Flow. A key challenge is the lack of hypercontractivity, which we overcome deriving new moment estimates.