User-Friendly Tail Bounds for Sums of Random Matrices
نویسندگان
چکیده
منابع مشابه
User-Friendly Tail Bounds for Sums of Random Matrices
This work presents probability inequalities for sums of independent, random, selfadjoint matrices. The results frame simple, easily verifiable hypotheses on the summands, and they yield strong conclusions about the large-deviation behavior of the maximum eigenvalue of the sum. Tail bounds for the norm of a sum of rectangular matrices follow as an immediate corollary, and similar techniques yiel...
متن کاملUser-friendly Tail Bounds for Matrix Martingales
This report presents probability inequalities for sums of adapted sequences of random, self-adjoint matrices. The results frame simple, easily verifiable hypotheses on the summands, and they yield strong conclusions about the large-deviation behavior of the maximum eigenvalue of the sum. The methods also specialize to sums of independent random matrices. 1. Main Results This technical report is...
متن کاملDimension-free tail inequalities for sums of random matrices
We derive exponential tail inequalities for sums of random matrices with no dependence on the explicit matrix dimensions. These are similar to the matrix versions of the Chernoff bound and Bernstein inequality except with the explicit matrix dimensions replaced by a trace quantity that can be small even when the dimension is large or infinite. Some applications to principal component analysis a...
متن کاملRandom Matrices: Tail Bounds for Gaps between Eigenvalues
Gaps (or spacings) between consecutive eigenvalues are a central topic in random matrix theory. The goal of this paper is to study the tail distribution of these gaps in various random matrix models. We give the first repulsion bound for random matrices with discrete entries and the first super-polynomial bound on the probability that a random graph has simple spectrum, along with several appli...
متن کاملUser-Friendly Tools for Random Matrices: An Introduction
Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including s...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Foundations of Computational Mathematics
سال: 2011
ISSN: 1615-3375,1615-3383
DOI: 10.1007/s10208-011-9099-z