Young Researchers Workshop: Kinetic theory with applications in physical sciences

The Parisi variational problem

Ian Tobasco

New York University

We introduce and study some basic questions regarding the phase diagram for mixed p-spin glasses. We focus on the analysis of the Parisi functional, a non-local, convex functional whose value is given by the solution of a certain Hamilton-Jacobi-Bellman PDE. We present a new characterization of minimizers, and use this to study the phase diagram in the temperature-external field plane. In particular, we present some recent progress on the Replica Symmetric-to-Replica Symmetry Breaking phase transition. This is joint work with Aukosh Jagannath (NYU).