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SpringerBriefs in Probability and Mathematical Statistics

Mod-ϕ Convergence

Normality Zones and Precise Deviations

Authors: Feray, Valentin, Meliot, Pierre-Loic, Nikeghbali, Ashkan

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  • First of its kind publication detailing the mod-ϕ convergence method
  • Written by leading experts in probability theory
  • Provides a large number of new results
  • Includes new examples coming from various areas of mathematics such as probability theory, number theory, combinatorics, and random matrix theory
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  • ISBN 978-3-319-46822-8
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Softcover $54.99
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  • ISBN 978-3-319-46821-1
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About this book

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. 

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)

Table of contents (11 chapters)

Table of contents (11 chapters)

Buy this book

eBook $39.99
price for USA in USD
  • ISBN 978-3-319-46822-8
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $54.99
price for USA in USD
  • ISBN 978-3-319-46821-1
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Mod-ϕ Convergence
Book Subtitle
Normality Zones and Precise Deviations
Authors
Series Title
SpringerBriefs in Probability and Mathematical Statistics
Copyright
2016
Publisher
Springer International Publishing
Copyright Holder
The Author(s)
eBook ISBN
978-3-319-46822-8
DOI
10.1007/978-3-319-46822-8
Softcover ISBN
978-3-319-46821-1
Series ISSN
2365-4333
Edition Number
1
Number of Pages
XII, 152
Number of Illustrations
8 b/w illustrations, 9 illustrations in colour
Topics

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