LA Probability Forum

Series: Caltech/UCLA Joint Probability Seminar Series

Spectral stability under real random absolutely continuous perturbations

Jorge Garza Vargas, Department of Computing and Mathematical Sciences, Caltech,

USC Kaprelian (KAP) 414

In this talk I will discuss the following random matrix phenomenon (relevant in the design of numerical linear algebra algorithms): 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 conretely, 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 (small) random matrix with independent real entries, each with absolutely continuous distributions. I will also mention follow up work and open questions.

This is joint work with Jess Banks, Archit Kulkarni and Nikhil Srivastava.

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