期刊
FOUNDATIONS OF COMPUTATIONAL MATHEMATICS
卷 12, 期 4, 页码 389-434出版社
SPRINGER
DOI: 10.1007/s10208-011-9099-z
关键词
Discrete-time martingale; Large deviation; Probability inequality; Random matrix; Sum of independent random variables
资金
- ONR [N00014-08-1-0883]
- DARPA [N66001-08-1-2065]
- AFOSR [FA9550-09-1-0643]
This paper presents new probability inequalities for sums of independent, random, self-adjoint matrices. These results place simple and easily verifiable hypotheses on the summands, and they deliver strong conclusions about the large-deviation behavior of the maximum eigenvalue of the sum. Tail bounds for the norm of a sum of random rectangular matrices follow as an immediate corollary. The proof techniques also yield some information about matrix-valued martingales. In other words, this paper provides noncommutative generalizations of the classical bounds associated with the names Azuma, Bennett, Bernstein, Chernoff, Hoeffding, and McDiarmid. The matrix inequalities promise the same diversity of application, ease of use, and strength of conclusion that have made the scalar inequalities so valuable.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据