Sharp asymptotics for the partition function of some continuous-time directed polymers

TL;DR

This paper derives sharp asymptotic estimates for the partition functions of certain continuous-time directed polymers in random environments, revealing detailed behavior of free energy and disorder regimes using Gaussian techniques.

Contribution

It introduces precise asymptotic analysis of partition functions for continuous-time directed polymers in space-time Gaussian environments, advancing understanding of their disorder regimes.

Findings

Asymptotic formulas for free energy at low temperature

Characterization of strong disorder regime

Application of Gaussian tools to polymer models

Abstract

This paper is concerned with two related types of directed polymers in a random medium. The first one is a d-dimensional Brownian motion living in a random environment which is Brownian in time and homogeneous in space. The second is a continuous-time random walk on the lattice Z^d, in a random environment with similar properties as in continuous space. The case of a space-time white noise environment can be acheived in this second setting. By means of some Gaussian tools, we estimate the free energy of these models at low temperature, and give some further information on the strong disorder regime of the objects under consideration.