How to free the boundary

schedule le lundi 05 novembre 2018 de 17h00 à 18h00

Organisé par : G. Conchon-Kerjan, F. Coppini, B. Dembin

Intervenant : Clément Cosco (LPSM)
Lieu : Salle 1016, Bâtiment Sophie Germain, Paris 7 Diderot

Sujet : How to free the boundary

Résumé :

Polymer models in random environment describe the behavior of long chains of monomers, dipped in an environment which interacts with them. In this talk, we consider a specific model called the Log-Gamma polymer. This model, on which we impose some boundary conditions, is solvable (one can compute many quantities that are usually out of reach in other models). Once the boundary conditions are freed, it was proved that the model features non-standard critical exponents and limiting laws. In fact, it is conjectured that under some conditions on the environment, all polymer models should have these same features (this is also called the KPZ universality conjecture). Although we know many things about the Log-Gamma polymer with boundary conditions, the process of freeing the conditions is non-trivial. Thus, a natural approach is to try to find a modification the model that mimics the process of removal, while still keeping its solvability. We will present a way of doing this, which we thoroughly called the Half-Log-Gamma polymer with boundary conditions, and we will state a few results about it.

(Joint work with Christopher Janjigian)