CMSA Probability Seminar: Sampling from the SK and mixed p-spin measures with stochastic localization

I will present an algorithm which efficiently samples from the Sherrington-Kirkpatrick (SK) measure with no external field at high temperature. The approach is based on the stochastic localization process of Eldan, together with a subroutine for computing the mean vectors of a family of measures tilted by an appropriate external field. Conversely, we show that no 'stable' algorithm can approximately sample from the SK measure at low temperature. Time permitting, we discuss extensions to the p-spin model.

This is based on a joint work with Andrea Montanari and Mark Sellke.