An Introduction to Matrix Concentration Inequalities
It makes advanced random matrix theory accessible to non-experts, though it is incremental in compiling existing methods.
The monograph introduces matrix concentration inequalities as a method to simplify solving challenging problems in random matrix theory, enabling solutions with minimal arithmetic.
In recent years, random matrices have come to play a major role in computational mathematics, but most of the classical areas of random matrix theory remain the province of experts. Over the last decade, with the advent of matrix concentration inequalities, research has advanced to the point where we can conquer many (formerly) challenging problems with a page or two of arithmetic. The aim of this monograph is to describe the most successful methods from this area along with some interesting examples that these techniques can illuminate.