Colloquium in Mathematics
Cancelled
Event details
| Date | 20.01.2025 |
| Hour | 13:30 › 14:30 |
| 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 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.
Please register on the following form : https://forms.gle/RXL5gkWLWSgwMayr6
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.
Please register on the following form : https://forms.gle/RXL5gkWLWSgwMayr6
Practical information
- Informed public
- Registration required
- This event is internal
Organizer
- Institute of Mathematic
Contact
- Prof. Laura Grigori
Prof. Daniel Kressner