Sampling, counting, and local central limit theorems

Abstract

I will describe how local central limit theorems (and Fourier-analytic proofs of local central limit theorems) can be used to design fast sampling algorithms and deterministic approximate counting algorithms for the number of independent sets and matchings of a given size in bounded degree graphs. Joint work with Vishesh Jain, Ashwin Sah, and Mehtaab Sawhney.