Year: 2025
Type: article
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.
DOI: 10.1214/25-aap2182
Institutions: University of Milano-Bicocca, University of Luxembourg
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4413182557