Defesa de Tese.

Banca examinadora: Hubert Lacoin - Orientador - IMPA Claudio Landim - IMPA MIlton Jara - IMPA Tertuliano Franco - (UFBA) Cyril Labbé - (Université Paris Dauphine) Augusto Teixeira - Suplente - IMPA

Abstract: This thesis studies the total variation mixing times for the heat-bath dynamics of two interface models and a particle system. The first interface model we consider is the polymer pinning model interacting with an impenetrable defected line, and in the repulsive phase we show that the total variation distance to equilibrium abruptly drops from one to zero. The other interface model is a variant of the polymer pinning model which is also subjected to another external force pulling the interface away from the defected line. We identify the localized/delocalized phase for the statics, and for the dynamics we identify the slow/rapidly mixing phase where the mixing time grows polynomially/superpolynomially. Finally, we study the asymmetric simple exclusion process in a random environment where the jump rates of particles are independently sampled from a common law. Assuming that the random environment is transient to the right, we prove that the mixing time of the process grows polynomially with high probability .