##### Department of Mathematics,

University of California San Diego

****************************

### Math 288 - Probability Seminar

## Nikhil Srivastava

#### UC Berkeley

## Concentration for Sums of Random Matrices with Markov Dependence

##### Abstract:

There are many well-known concentration results for sums of independent random matrices, e.g. those of Rudelson, Ahlswede-Winter, Tropp, and Oliveira. We move beyond the independent setting, and prove a Chernoff-type bound for sums of matrix-valued random variables sampled via a random walk on an reversible Markov chain, confirming a conjecture due to Wigderson and Xiao. Our proof is based on a new multi-matrix extension of the Golden-Thompson inequality which follows from complex interpolation methods. Joint work with A. Garg, Y. Lee, and Z. Song.

Host: Todd Kemp

### September 27, 2018

### 11:00 AM

### AP&M 6402

****************************