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.

This talk has been canceled/deleted

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 \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{\circ}-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:

This talk is not included in any other list

Note that ex-directory lists are not shown.


© 2006-2019, University of Cambridge. Contact Us | Help and Documentation | Privacy and Publicity