Cutoff for polymer pinning dynamics in the repulsive phase




报告摘要:We consider the Glauber dynamics for a model of polymer interacting with a substrate or wall. The state space is the set of one-dimensional nearest-neighbor paths with nonnegative integer coordinates, starting at the x-axis and coming back tothe x-axis after L steps and the Gibbs weight of a path is given by a#contacts, where a is a positive parameter which models the intensity of the interaction with the substrate. The dynamics proceeds by updating each coordinate with rate one in a heat-bath fashion. This model was introduced by Caputo et al with the aim of studying the relaxation to equilibrium of the system.

We present new results concerning the total variation mixing time for this dynamic when a<2, which corresponds to the phase where the effects of the wall's entropic repulsion dominates, improving results by Caputo et al.