Mathematics Colloquium
Event details
| Date | 17.06.2026 |
| Hour | 16:15 › 17:15 |
| Speaker | Prof. Joel A. Tropp, Steele Family Professor of Applied & Computational Mathematics, Caltech |
| Location | |
| Category | Conferences - Seminars |
| Event Language | English |
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, a similar 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 targets a general mathematical audience.
Preprint: https://arxiv.org/abs/2501.16578
Please register on the following form : https://forms.gle/ppXwKo9HmTgFk3rc7
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, a similar 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 targets a general mathematical audience.
Preprint: https://arxiv.org/abs/2501.16578
Please register on the following form : https://forms.gle/ppXwKo9HmTgFk3rc7
Practical information
- Informed public
- Invitation required
- This event is internal
Organizer
- Prof. Nicolas Boumal
Contact
- Institute of Mathematics