University of Cambridge > > 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

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.

Tell a friend about this talk:

This talk is included in these lists:

Note that ex-directory lists are not shown.


© 2006-2020, University of Cambridge. Contact Us | Help and Documentation | Privacy and Publicity