The critical curve for pinning of random polymers. A large deviations approach

The critical curve for pinning of random polymers. A large deviations approach

Mon, 15/11/2010
14:15 		Dimitris Cheliotis Stochastic Analysis Seminar Add to calendar Eagle House
The critical curve for pinning of random polymers. A large deviations approach
We consider a directed random polymer interacting with an interface that carries random charges some of which attract while others repel the polymer. Such a polymer can be in a localized or delocalized phase, i.e., it stays near the interface or wanders away respectively.  The phase it chooses depends on the temperature and the average bias of the disorder. At a given temperature, there is a critical bias separating the two phases. A question of particular interest, and which has been studied extensively in the Physics and Mathematics literature, is whether the quenched critical bias differs from the annealed critical bias. When it does, we say that the disorder is relevant. Using a large deviations result proved recently by Birkner, Greven, and den Hollander, we derive a variational formula for the quenchedcritical bias. This leads to a necessary and sufficient condition for disorder relevance that implies easily some known results as well as new ones. The talk is based on joint work with Frank den  Hollander.