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Freedman's inequality for matrix martingales

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Freedman's inequality for matrix martingales
2.	Creator	Author's name, affiliation, country	Joel A Tropp; California Institute of Technology
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Discrete-time martingale, large deviation, probability inequality, random matrix
3.	Subject	Subject classification	60B20; 60F10; 60G42.
4.	Description	Abstract	Freedman's inequality is a martingale counterpart to Bernstein's inequality. This result shows that the large-deviation behavior of a martingale is controlled by the predictable quadratic variation and a uniform upper bound for the martingale difference sequence. Oliveira has recently established a natural extension of Freedman's inequality that provides tail bounds for the maximum singular value of a matrix-valued martingale. This note describes a different proof of the matrix Freedman inequality that depends on a deep theorem of Lieb from matrix analysis. This argument delivers sharp constants in the matrix Freedman inequality, and it also yields tail bounds for other types of matrix martingales. The new techniques are adapted from recent work by the present author.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)	AFOSR; ONR.
7.	Date	(YYYY-MM-DD)	2011-05-23
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ecp.ejpecp.org/article/view/1624
10.	Identifier	Digital Object Identifier	10.1214/ECP.v16-1624
11.	Source	Journal/conference title; vol., no. (year)	Electronic Communications in Probability; Vol 16
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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