The Intermediate Disorder Regime for Brownian Directed Polymers in Poisson Environment

2018/04/25 by Cosco, Clément
#60F05 #82D60 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)

paper · doi:10.48550/arxiv.1804.09571

Abstract

We consider the Brownian directed polymer in Poissonian environment in dimension 1+1, under the so-called intermediate disorder regime, which is a crossover regime between the strong and weak disorder regions. We show that, under a diffusive scaling involving different parameters of the system, the renormalized point-to-point partition function of the polymer converges in law to the solution of the stochastic heat equation with Gaussian multiplicative noise. The Poissonian environment provides a natural setting and strong tools, such as the Wiener-Ito chaos expansion, which, applied to the partition function, is the basic ingredient of the proof.

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