# Student Probability Seminar

#### Dynamics of Mean-Field Spin Glasses I

**Speaker:**
Reza Gheissari

**Location:**
Warren Weaver Hall 805

**Date:**
Thursday, February 22, 2018, 11 a.m.

**Synopsis:**

*We will introduce several models of mean-field spin glasses, beginning with the toy model of the random energy model, then defining the p-spin glass models on the hypercube and sphere. We define some dynamics for these models, focusing on the Glauber dynamics for discrete models and it’s analogue, Langevin dynamics, for spherical models. We then discuss the relation between the dynamical behavior of these models and their static replica symmetry phase transition, as well as the complexity of the energy landscape. We motivate the idea of aging, known rigorously in some settings, and demonstrate a dynamical transition between high and low temperatures in the equilibriation time of these dynamics. *