Mod-ϕ Convergence

Normality Zones and Precise Deviations

Nonfiction, Science & Nature, Mathematics, Number Theory, Statistics
Cover of the book Mod-ϕ Convergence by Ashkan Nikeghbali, Valentin Féray, Pierre-Loïc Méliot, Springer International Publishing
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Author: Ashkan Nikeghbali, Valentin Féray, Pierre-Loïc Méliot ISBN: 9783319468228
Publisher: Springer International Publishing Publication: December 6, 2016
Imprint: Springer Language: English
Author: Ashkan Nikeghbali, Valentin Féray, Pierre-Loïc Méliot
ISBN: 9783319468228
Publisher: Springer International Publishing
Publication: December 6, 2016
Imprint: Springer
Language: English

The canonical way to establish the central limit theorem for i.i.d. random variables is to use characteristic functions and Lévy’s continuity theorem. This monograph focuses on this characteristic function 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. 

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The canonical way to establish the central limit theorem for i.i.d. random variables is to use characteristic functions and Lévy’s continuity theorem. This monograph focuses on this characteristic function 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. 

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