# Stein’s method for concentration inequalities

@article{Chatterjee2006SteinsMF, title={Stein’s method for concentration inequalities}, author={Sourav Chatterjee}, journal={Probability Theory and Related Fields}, year={2006}, volume={138}, pages={305-321} }

We introduce a version of Stein’s method for proving concentration and moment inequalities in problems with dependence. Simple illustrative examples from combinatorics, physics, and mathematical statistics are provided.

## 113 Citations

Stein ’ s method for concentration inequalities

- Mathematics
- 2007

We introduce a version of Stein’s method for proving concentration and moment inequalities in problems with dependence. Simple illustrative examples from combinatorics, physics, and mathematical…

Efron–Stein inequalities for random matrices

- Mathematics
- 2014

This paper establishes new concentration inequalities for random matrices constructed from independent random variables. These results are analogous with the generalized Efron–Stein inequalities…

Transport inequalities and Concentration of measure

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- 2015

We give a short introduction to the concentration of measure phenomenon and connect it with dierent functional inequalities (Poincare, Talagrand and Log-Sobolev inequalities). Resume. Nous presentons…

A ug 2 01 4 Efron – Stein Inequalities for Random Matrices

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- 2014

This paper establishes new concentration inequalities for random matrices constructed from independent random variables. These results are analogous with the generalized Efron–Stein inequalities…

Subadditivity of Matrix phi-Entropy and Concentration of Random Matrices

- Mathematics, Computer ScienceArXiv
- 2013

It is demonstrated that a class of entropy functionals defined for random matrices satisfy a subadditivity property, and several matrix concentration inequalities are derived as an application of this result.

Applications of Stein's method for concentration inequalities

- Mathematics
- 2010

Stein’s method for concentration inequalities was introduced to prove concentration of measure in problems involving complex dependencies such as random permutations and Gibbs measures. In this…

Concentration of Measure

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- 2014

Concentration of measure plays a central role in the content of this book. This chapter gives the first account of this subject. Bernstein-type concentration inequalities are often used to…

Concentration of measure principle and entropy-inequalities

- Mathematics
- 2017

The concentration measure principle is presented in an abstract way to encompass and unify different concentration properties. We give a general overview of the links between concentration…

Stein's method for dynamical systems

- Mathematics
- 2017

We present an adaptation of Stein's method of normal approximation to the study of both discrete- and continuous-time dynamical systems. We obtain new correlation-decay conditions on dynamical…

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Large deviation estimates are derived for sums of random variables with certain dependence structures, including finite population statistics and random graphs. The argument is based on Stein's…

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Let W be either the number of descents or inversions of a permutation. Stein's method is applied to show that W satisfies a central limit theorem with error rate n^(-1/2). The construction of an…

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SummaryStein's method of obtaining distributional approximations is developed in the context of functional approximation by the Wiener process and other Gaussian processes. An appropriate analogue of…

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A Berry-Esseen theorem for the rate of convergence of general nonlinear multivariate sampling statistics with normal limit distribution is derived via a multivariate extension of Stein's method. The…

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We investigate a new methodology, worked out by Ledoux and Massart, to prove concentration-of-measure inequalities. The method is based on certain modified logarithmic Sobolev inequalities. We…