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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  • HAL Id : hal-00704994, version 2

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

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