Palestrante: Hubert Lacoin
Insituição: IMPA

The Directed Polymer in a Random Environment is a statistical mechanics model, which has been introduced (in dimension 1) as a toy model to study the interfaces of the planar Ising model with random coupling constants. The model was shortly afterwards generalized to higher dimensions. In this latter case, rather than an effective interface model, the directed polymer in a random environment can be thought of as modeling the behavior of a stretched polymer in a solution with impurities. The interest in the model model, triggered by its rich phenomenology,  has since then generated a plentiful literature in theoretical physics and mathematics. 

As for many models in statistical mechanics, the directed polymer's behavior is very much related to that of the partition function of the model which is defined as the sum of the Gibbs weight amongst all possible configurations. Depending on whether the partition function concentrates around its mean value or not, the polymer will exhibit a localized or delocalized behavior.
This talk will be dedicated to the exploration of this relation between partition function and polymer behavior and to the exposition of recently obtained results concerning the sharpness and regularity of the phase transition.