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© 2016

Mod-ϕ Convergence

Normality Zones and Precise Deviations

Book

Table of contents

  1. Front Matter
    Pages i-xii
  2. Valentin Féray, Pierre-Loïc Méliot, Ashkan Nikeghbali
    Pages 1-8
  3. Valentin Féray, Pierre-Loïc Méliot, Ashkan Nikeghbali
    Pages 9-16
  4. Valentin Féray, Pierre-Loïc Méliot, Ashkan Nikeghbali
    Pages 17-32
  5. Valentin Féray, Pierre-Loïc Méliot, Ashkan Nikeghbali
    Pages 33-50
  6. Valentin Féray, Pierre-Loïc Méliot, Ashkan Nikeghbali
    Pages 51-58
  7. Valentin Féray, Pierre-Loïc Méliot, Ashkan Nikeghbali
    Pages 59-64
  8. Valentin Féray, Pierre-Loïc Méliot, Ashkan Nikeghbali
    Pages 65-86
  9. Valentin Féray, Pierre-Loïc Méliot, Ashkan Nikeghbali
    Pages 87-94
  10. Valentin Féray, Pierre-Loïc Méliot, Ashkan Nikeghbali
    Pages 95-110
  11. Valentin Féray, Pierre-Loïc Méliot, Ashkan Nikeghbali
    Pages 111-122
  12. Valentin Féray, Pierre-Loïc Méliot, Ashkan Nikeghbali
    Pages 123-139
  13. Back Matter
    Pages 141-152

About this book

Introduction

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. 

Keywords

Probability Theory Number Theory Combinatorics Matrix Theory Deviations

Authors and affiliations

  1. 1.Institut für MathematikUniversität Zürich — WinterthurerstrasseZürichSwitzerland
  2. 2.Laboratoire de Mathématiques, Bâtiment 425 — Faculté Des Sciencesd’Orsay—Université Paris-SudOrsayFrance
  3. 3.Institut für MathematikUniversität Zürich — WinterthurerstrasseZürichSwitzerland

Bibliographic information

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Reviews

“The book is well written and mathematically rigorous. They authors collect a large variety of results and try to parallel the theory with applications and they do this rather successfully. It may become a standard reference for researchers working on the topic of central limit theorems and large deviation. … this is a useful book for a researcher in probability theory and mathematical statistics. It is very carefully written and collects many new results.” (Nikolai N. Leonenko, zbMATH 1387.60003, 2018)

“This beautiful book (together with other publications by these authors) opens a new way of proving limit theorems in probability theory and related areas such as probabilistic number theory, combinatorics, and statistical mechanics. It will be useful to researchers in these and many other areas.” (Zakhar Kabluchko, Mathematical Reviews, September, 2017)