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Probability and Combinatorics

Tuesday, October 12, 2021 - 3:30pm

Robert Hough

Stony Brook University


University of Pennsylvania

David Rittenhouse Lab A-1

Alexopoulos proved local limit theorems for measures with a density and lattice measures in the general setting of groups of moderate growth. On the Heisenberg group, Breuillard's thesis obtained a local limit theorem for general measures subject to a condition on the characteristic function, and asked if this condition can be removed. I will discuss two new local limit theorems, one joint with Diaconis, that treat local limit theorems on nilpotent Lie groups driven by general measures. We prove Breuillard's conjecture and also solve a problem of Diaconis and Saloff-Coste on the mixing of the central coordinate in unipotent matrix walks modulo $p$.