Probability Seminar

Title: Efficient sampling from the Continuous Random Energy Model.

Abstract: The Continuous Random Energy Model (CREM) is a hierarchical Gaussian field on the leaves of a binary tree. Given a realization of this random landscape, we ask whether one can sample efficiently from its Gibbs measure, in total variation distance, without examining all exponentially many leaves. I will describe two polynomial-time sampling algorithms below an explicit high-temperature threshold: a Metropolis chain on the full tree and a sequential sampler using logarithmic lookahead. Their analysis relies on quantitative analysis of normalized partition functions and a contiguity argument for the tilted environment observed along a Gibbs-sampled path. Interestingly, efficient fixed-accuracy sampling can hold even when the global spectral gap is exponentially small. This is joint work with Holden Lee (JHU).