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University of Cambridge > Talks.cam > Probability > Directed polymers in random environment with heavy tails.

## Directed polymers in random environment with heavy tails.Add to your list(s) Download to your calendar using vCal - Oren Louidor (NYU)
- Friday 04 December 2009, 14:30-15:30
- Seminar Room 2, Newton Institute Gatehouse..
If you have a question about this talk, please contact Berestycki. We study the model of Directed Polymers in Random Environment in 1+1 dimensions, where the environment is i.i.d. with a site distribution having a tail that decays regularly polynomially with power -\alpha, where \alpha \in (0,2). After proper scaling of temperature 1/\beta, we show strong localization of the polymer to an optimal region in the environment where energy and entropy are best balanced. We prove that this region has a weak limit under linear scaling and identify the limiting distribution as an (\alpha, \beta)-indexed family of measures on Lipschitz curves lying inside the 45’-rotated square with unit diagonal. In particular, this shows order of n for the transversal fluctuations of the polymer. If (and only if) \alpha is small enough, we find that there exists a random critical temperature above which the effect of the environment is not macroscopically noticeable. The results carry over to higher dimensions with minor modifications. Joint work with A. Auffinger . This talk is part of the Probability series. ## This talk is included in these lists:- All CMS events
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