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arXiv · 2307.02453

Quasi-critical fluctuations for 2d directed polymers

Francesco Caravenna·Francesca Cottini·Maurizia Rossi
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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.

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Francesco Caravenna, Francesca Cottini, Maurizia Rossi. 2023-07-05. Quasi-critical fluctuations for 2d directed polymers. https://arxiv.org/abs/2307.02453

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