A new look at independence

Michel Talagrand

Type: Article

Publication Date: 1996-01-01

Citations: 353

DOI: https://doi.org/10.1214/aop/1042644705

Abstract

The concentration of measure phenomenon is product spaces is a far-reaching abstract generalization of the classical exponential inequalities for sums of independent random variables. We attempt to explain in the simplest possible terms the basic concepts underlying this phenomenon, the basic method to prove concentration inequalities and the meaning of several of the most useful inequalities.

Locations

The Annals of Probability - View - PDF

Similar Works

Action	Title	Year	Authors
+	Concentration inequalities : a non asymptotic theory of independence	2013	Stéphane Boucheron Gábor Lugosi Pascal Massart
+	Concentration inequalities. A nonasymptotic theory of independence	2013	Stéphane Boucheron Gábor Lugosi Pascal Massart
+ PDF Chat	Concentration Inequalities	2004	Stéphane Boucheron Gábor Lugosi Olivier Bousquet
+	Statistical Independence	2023	Kenneth W. Shum
+	Dependence Concepts and Probability Inequalities	1975	Kumar Jogdeo
+	THE INDEPENDENCE THEOREM	2011	Enrique Casanovas
+	A concentration inequality for product spaces	2014	Pandelis Dodos Vassilis Kanellopoulos Konstantinos Tyros
+	A concentration inequality for product spaces	2015	Pandelis Dodos Vassilis Kanellopoulos Konstantinos Tyros
+	A concentration inequality for product spaces	2014	Pandelis Dodos Vassilis Kanellopoulos Konstantinos Tyros
+	Introduction to Probability	2022	Robert G. Underwood
+	The Borel-Cantelli Lemma	2012	Tapas K. Chandra
+ PDF Chat	Concentration of Measure Without Independence: A Unified Approach Via the Martingale Method	2017	Aryeh Kontorovich Maxim Raginsky
+	Concentration of measure without independence: a unified approach via the martingale method	2016	Aryeh Kontorovich Maxim Raginsky
+	Concentration, Results and Applications	2003	Gideon Schechtman
+ PDF Chat	Probability Theory	2013	R. P. Pakshirajan
+ PDF Chat	Concentration Inequalities	2001	Luc Devroye Gábor Lugosi
+	A Note on the Product Borel Probability Measure	2006	Ma Dong-kui Xu Xu Zhi-ting
+ PDF Chat	On a concentration inequality for sums of independent isotropic vectors	2012	M. Cranston Stanislav Molchanov
+	A Note on the Probabilistic Inequalities	1961	H. P. Kuang
+	A Note on the Probabilistic Inequalities	1961	H. P. Kuang

Works That Cite This (276)

Action	Title	Year	Authors
+	The Martingale Approach for Concentration and Applications in Information Theory, Communications and Coding	2012	Igal Sason
+	Rate of convergence of the mean for sub-additive ergodic sequences	2014	Antonio Auffinger Michael Damron Jack Hanson
+	Tail index estimation, concentration and adaptivity	2015	Stéphane Boucheron Maud Thomas
+ PDF Chat	Non-asymptotic Theory of Random Matrices: Extreme Singular Values	2011	Mark Rudelson Roman Vershynin
+	Random perturbation of low rank matrices: Improving classical bounds	2017	Sean O’Rourke Van Vu Ke Wang
+ PDF Chat	Measure concentration for a class of random processes	1998	K. Marton
+ PDF Chat	On dimension-dependent concentration for convex Lipschitz functions in product spaces	2023	Han Huang Konstantin Tikhomirov
+ PDF Chat	Targeted Maximum Likelihood Learning	2006	Mark J. van der Laan Daniel B. Rubin
+	Concentration inequalities for random tensors	2019	Roman Vershynin
+ PDF Chat	Threshold for monotone symmetric properties through a logarithmic Sobolev inequality	2006	Raphaël Rossignol

Works Cited by This (11)

Action	Title	Year	Authors
+ PDF Chat	Asymptotic Theory of Finite Dimensional Normed Spaces	1986	Vitali Milman Gideon Schechtman
+ PDF Chat	Probability in Banach Spaces	1976	Michel Ledoux Michel Talagrand
+	A conjecture on convolution operators, and a non-Dunford-Pettis operator onL 1	1989	Michel Talagrand
+ PDF Chat	On proof and progress in mathematics	1994	William P. Thurston
+	A Topological Application of the Isoperimetric Inequality	1983	M. Gromov Vitali Milman
+ PDF Chat	The Height of a Random Partial Order: Concentration of Measure	1992	Béla Bollobás Graham Brightwell
+ PDF Chat	Regularity of gaussian processes	1987	Michel Talagrand
+	Isoperimetry, logarithmic sobolev inequalities on the discrete cube, and margulis' graph connectivity theorem	1993	Michel Talagrand
+	Unconditional and symmetric sets inn-dimensional normed spaces	1980	D. Amir Vitali Milman
+	The Supremum of Some Canonical Processes	1994	Michel Talagrand