# Localization Transition for Polymers in Poissonian Medium

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 $\beta$.
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Cited literature [39 references]

https://hal.archives-ouvertes.fr/hal-00704994
Contributor : Francis Comets <>
Submitted on : Thursday, September 24, 2015 - 10:18:03 AM
Last modification on : Thursday, March 21, 2019 - 1:05:59 PM
Long-term archiving on: Wednesday, April 26, 2017 - 6:43:42 PM

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b^2nu.pdf
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• HAL Id : hal-00704994, version 2

### Citation

Francis Comets, Nobuo Yoshida. Localization Transition for Polymers in Poissonian Medium. 2012. ⟨hal-00704994v2⟩

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