Tutorial - User-friendly tail bound for sums of random matrices
Presenter
September 27, 2011
Keywords:
- Random matrices
MSC:
- 15B52
Abstract
We introduce a new methodology for studying the maximum eigenvalue of a sum of independent, symmetric random matrices. This approach results in a complete set of extensions to the classical tail bounds associated with the names Azuma, Bennett, Bernstein, Chernoff, Freedman, Hoeffding, and McDiarmid. Results for rectangular random matrices follow as a corollary. This research is inspired by the work of Ahlswede--Winter and Rudelson--Vershynin, but the new methods yield essential improvements over earlier results. We believe that these techniques have the potential to simplify the study a large class of random matrices.