Quasi-critical fluctuations for 2d directed polymers

2023/07/05 by Caravenna, Francesco, Cottini, Francesca, Rossi, Maurizia · 5 citations
#35R60 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Primary: 82B44 #Probability (math.PR) #Secondary: 60F05

paper · doi:10.48550/arxiv.2307.02453

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.

Cited by

• From disordered systems to the Critical 2D Stochastic Heat Flow
• Non-coincidence of critical points for directed polymers on supercritical percolation clusters
• A central limit theorem for two-dimensional directed polymers with critical spatial correlation
• Strong Disorder for Stochastic Heat Flow and 2D Directed Polymers
• Enhanced noise sensitivity, 2D directed polymers and Stochastic Heat Flow

Related

• The Critical 2d Stochastic Heat Flow
• The Critical 2d Stochastic Heat Flow and Related Models
• High moments of 2d directed polymers up to quasi-criticality
• Strong Disorder for Stochastic Heat Flow and 2D Directed Polymers
• Gaussian fluctuations for the directed polymer partition function for d≥ 3 and in the whole L²-region