The intermediate disorder regime for stable directed polymer in Poisson environment

2024/01/09 by Wang, Min
#60K35 #60K37 #82D60 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2401.04459

Abstract

We consider the stable directed polymer in Poisson random environment in dimension 1+1, under the intermediate disorder regime. We show that, under a diffusive scaling involving different parameters of the system, the normalized point-to-point partition function of the polymer converges in law to the solution of the stochastic heat equation with fractional Laplacian and Gaussian multiplicative noise.

Related

• The Intermediate Disorder Regime for Brownian Directed Polymers in Poisson Environment
• Intermediate Disorder regime for half-space directed polymers
• From Directed Polymers in Spatial-correlated Environment to Stochastic Heat Equations Driven by Fractional Noise in 1 + 1 Dimensions
• Central limit theorems for the (2+1)-dimensional directed polymer in the weak disorder limit
• Scaling limit of a directed polymer among a Poisson field of independent walks