Localization Transition for Polymers in Poissonian Medium

TL;DR

This paper investigates the phase transitions and localization phenomena of directed polymers in a Poissonian random environment, providing detailed phase diagrams and conditions for localization based on environment density and temperature.

Contribution

It offers new quantitative estimates on the critical curve and characterizes localization behavior in polymers within Poissonian media.

Findings

Quantitative estimates of the critical curve for phase transition.

Pathwise localization at low temperature or high density.

Complete localization in a preferred corridor for large eta^2 nd bounded eta.

Abstract

We study a model of directed polymers in random environment in dimension $1+d$, given by a Brownian motion in a Poissonian potential. We study the effect of the density and the strength of inhomogeneities, respectively the intensity parameter $\nu$ of the Poisson field and the temperature inverse $\beta$. Our results are: (i) fine information on the phase diagram, with quantitative estimates on the critical curve; (ii) pathwise localization at low temperature and/or large density; (iii) complete localization in a favourite corridor for large $\nu \beta^2$ and bounded $\beta$.