Title: Positive random walks and positive-semidefinite random matrices
Abstract: On the real line, a random walk that can only move in the positive direction is very unlikely to remain close to its origin. After a fixed number of steps, the left tail has a Gaussian profile under minimal assumptions. Remarkably, the same phenomenon occurs when we consider a positive random walk on the cone of positive-semidefinite matrices. After a fixed number of steps, the minimum eigenvalue is described by a Gaussian random matrix model.
This talk introduces a new way to make this intuition rigorous. The methodology addresses an open problem in computational mathematics about sparse random embeddings. The presentation is targeted at a general mathematical audience.
Preprint: https://arxiv.org/abs/2501.16578
10:30am - Pre-talk meet and greet teatime - 219 Prospect Street, 11 floor, there will be light snacks and beverages in the kitchen area. For more details and upcoming events visit our website at https://statistics.yale.edu/calendar.