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Mod-ϕ Convergence

Normality Zones and Precise Deviations

  • Valentin Féray
  • Pierre-Loïc Méliot
  • Ashkan Nikeghbali

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

  • Valentin Féray
    • 1
  • Pierre-Loïc Méliot
    • 2
  • Ashkan Nikeghbali
    • 3
  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

  • DOI https://doi.org/10.1007/978-3-319-46822-8
  • Copyright Information The Author(s) 2016
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-46821-1
  • Online ISBN 978-3-319-46822-8
  • Series Print ISSN 2365-4333
  • Series Online ISSN 2365-4341
  • Buy this book on publisher's site