Julien Poisat (Univ. Paris-Dauphine) : Phase transitions in charged polymer models

I will review some old and recent results on the topic of charged polymer models. Those are random walk models with disordered interaction at self-intersections, introduced by Kantor and Kardar in the 90’s. Precise results have been obtained so far for the one-dimensional model in the annealed setting, showing a phase transition from a collapsed phase (attractive interactions prevailing) to an extended phase (repulsive interactions prevailing). Those results have been then extended to higher dimensions, in a more qualitative way. I will also mention a variant model with quenched disorder, for which a freezing transition was conjectured by Derrida, Griffiths and Higgs. Based on joint works with Q. Berger, F. Caravenna, F. den Hollander and N. Pétrélis.