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Lectures Year : 2017

Basic Concentration Properties of Real-Valued Distributions

Odalric-Ambrym Maillard

Abstract

In this note we introduce and discuss a few concentration tools for the study of concentration inequalities on the real line. After recalling versions of the Chernoff method, we move to concentration inequalities for predictable processes. We especially focus on bounds that enable to handle the sum of real-valued random variables, where the number of summands is itself a random stopping time, and target fully explicit and empirical bounds. We then discuss some important other tools, such as the Laplace method and the transportation lemma.
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Dates and versions

cel-01632228 , version 1 (09-11-2017)

Identifiers

  • HAL Id : cel-01632228 , version 1

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Odalric-Ambrym Maillard. Basic Concentration Properties of Real-Valued Distributions. Doctoral. France. 2017. ⟨cel-01632228⟩
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