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AMS Special Seminar Series | Joel Tropp

October 16 @ 1:30 pm - 2:30 pm

Location: Krieger 205

When: October 16th at 1:30 p.m.

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 starting point. 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 also described by a Gaussian model.

This talk introduces a new way to make this intuition rigorous. The methodology provides the solution to 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

Zoom link: https://wse.zoom.us/j/93600407710?pwd=JBL8VsObRxX6MkhdjAUxCadqJDoZrZ.1

Details

Date:
October 16
Time:
1:30 pm - 2:30 pm
Event Category:

Venue

Krieger 205
3400 North Charles Street
Baltimore, Maryland 21218
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