Localization transition for polymers in Poissonian medium
Résumé
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 I-2 (2) and bounded beta.