California Institute of Technology - Computing & Mathematical Sciences
Random matrices now play a role in many areas of theoretical, applied, and computational mathematics. Therefore, it is desirable to have tools for studying random matrices that are flexible, easy to use, and powerful. Over the last fifteen years, researchers have developed a remarkable family of results, called matrix concentration inequalities, that balance these criteria.
This talk offers an invitation to the field of matrix concentration inequalities. The presentation begins with some history of random matrix theory, and it introduces an important probability inequality for scalar random variables. It describes a flexible model for random matrices that is suitable for many problems, and it discusses one of the most important matrix concentration results, the matrix Bernstein inequality. The talk concludes with some applications drawn from algorithms, combinatorics, statistics, signal processing, scientific computing, and beyond.