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Session II.5 - Random Matrices

Thursday, June 15, 15:00 ~ 15:30

Spectral stability under random perturbations

Jorge Garza-Vargas

Caltech, United States of America   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

In this talk I will discuss the following random matrix phenomenon (relevant in numerical diagonalization): if one adds independent (tiny) random variables to the entries of an arbitrary deterministic matrix A, with high probability, the resulting matrix A′ will have (relatively) stable eigenvenvalues and eigenvectors. More concretely, I will explain the key ideas behind obtaining tail bounds for the eigenvector condition number and minimum eigenvalue gap of a deterministic matrix that has been perturbed by a (tiny) random matrix with independent entries, each having an absolutely continuous distribution.

Joint work with Jess Banks (UC Berkeley), Archit Kulkarni (UC Berkeley) and Nikhil Srivastava (UC Berkeley).

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