Strong disorder implies strong localization for directed polymers in a random environment

TL;DR

This paper demonstrates that in any dimension, strong disorder in directed polymers within a random environment leads to strong localization, specifically proven for the continuous-time parabolic Anderson Model.

Contribution

It establishes a general link between strong disorder and strong localization for directed polymers, extending the understanding to the continuous-time parabolic Anderson Model.

Findings

Strong disorder implies strong localization in any dimension.

Proven for the continuous-time parabolic Anderson Model.

Provides theoretical insight into polymer behavior in random environments.

Abstract

In this note we show that in any dimension $d$, the strong disorder property implies the strong localization property. This is established for a continuous time model of directed polymers in a random environment : the parabolic Anderson Model.