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Mod-ϕ Convergence : Normality Zones and Precise Deviations

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概要 The canonical way to establish the central limit theorem for i.i.d. random variables is to use characteristic functions and Lv̌y’s continuity theorem. This monograph focuses on this characteristic fun...ction approach and presents a renormalization theory called mod-ϕ convergence. This type of convergence is a relatively new concept with many deep ramifications, and has not previously been published in a single accessible volume. The authors construct an extremely flexible framework using this concept in order to study limit theorems and large deviations for a number of probabilistic models related to classical probability, combinatorics, non-commutative random variables, as well as geometric and number-theoretical objects. Intended for researchers in probability theory, the text is carefully well-written and well-structured, containing a great amount of detail and interesting examples. .続きを見る
目次 Preface
Introduction
Preliminaries
Fluctuations in the case of lattice distributions
Fluctuations in the non-lattice case
An extended deviation result from bounds on cumulants
A precise version of the Ellis-Gr̃tner theorem
Examples with an explicit generating function
Mod-Gaussian convergence from a factorisation of the PGF
Dependency graphs and mod-Gaussian convergence
Subgraph count statistics in Erds̲-Rňyi random graphs
Random character values from central measures on partitions
Bibliography.
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本文を見る Full text available from Springer Mathematics and Statistics eBooks 2016 English/International

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登録日 2020.06.27
更新日 2020.06.28