Sharp asymptotics for the free energy of 1+1 dimensional directed polymers in an infinitely divisible environment

TL;DR

This paper extends known sharp estimates of the free energy for 1+1 dimensional directed polymers from Gaussian environments to those with infinitely divisible distributions, broadening the understanding of these models.

Contribution

It provides the first sharp asymptotic estimates for directed polymers in an infinitely divisible environment, generalizing previous Gaussian-specific results.

Findings

Established sharp free energy estimates for infinitely divisible environments

Extended Gaussian case results to a broader class of distributions

Enhanced understanding of directed polymer behavior in diverse environments

Abstract

We give sharp estimate for the free energy of directed polymers in random environment in dimension 1+1. This estimate was known for a Gaussian environment, we extend it to the case where the law of the environment is infinitely divisible.