On the Markus-Spielman-Srivastava inequality for sums of rank-one matrices

TL;DR

This paper extends the Markus-Spielman-Srivastava inequality to sums of rank-one matrices without requiring the matrices to be isotropic, broadening its applicability in random matrix theory.

Contribution

It introduces a generalized inequality for sums of rank-one matrices by relaxing the isotropy condition, advancing theoretical understanding in the field.

Findings

Extended the inequality to non-isotropic matrices

Provided bounds for sums of rank-one matrices

Broadened applicability of matrix concentration results

Abstract

We extend the result of Markus, Spielman, and Srivastava about the sum of rank-one symmetric random matrices to the case when the isotropy assumption on the random matrices is relaxed.