20/11/2024, 16:00 — 17:00 — Online
Milton Jara, Instituto de Matemática Pura e Aplicada
Sharp convergence for the stochastic Curie-Weiss model
The stochastic Curie-Weiss model is probably the simplest example of a non-trivial Glauber dynamics. This model has been extensively studied, and in the high-temperature regime, Levin-Luczak-Peres computed the mixing time up to an optimal constant of order O(n). In the classical definition of mixing time, one takes the least-favorable case as initial condition of the dynamics. A natural question to tackle is the dependence of the mixing time on the initial condition of the dynamics. In order to solve this question, we develop a new framework, which we call sharp convergence. We show sharp convergence of the Curie-Weiss model in the whole high-temperature regime, including non-zero magnetic field, and as an application we compute the mixing time of the Curie-Weiss model up to order o(n), and we also show that the mixing time improves if we take initial conditions with the ‘right’ density. Joint work with Freddy Hernández (Universidad Nacional de Colombia)
