The intermediate disorder regime for Brownian directed polymers in Poisson environment

We consider the Brownian directed polymer in Poissonian environment in dimension 1+1, under the so-called intermediate disorder regime (Alberts et al., 2014), 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 (Last and Penrose, 2017), which, applied to the partition function, is the basic ingredient of the proof. (C) 2019 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.