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SpringerBriefs in Probability and Mathematical Statistics

Mod-ϕ Convergence

Normality Zones and Precise Deviations

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

  • 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
Weitere Vorteile

Dieses Buch kaufen

eBook 41,64 €
Preis für Deutschland (Brutto)
  • ISBN 978-3-319-46822-8
  • Versehen mit digitalem Wasserzeichen, DRM-frei
  • Erhältliche Formate: PDF, EPUB
  • eBooks sind auf allen Endgeräten nutzbar
  • Sofortiger eBook Download nach Kauf
Softcover 53,49 €
Preis für Deutschland (Brutto)
  • ISBN 978-3-319-46821-1
  • Kostenfreier Versand für Individualkunden weltweit
  • Gewöhnlich versandfertig in 3-5 Werktagen.
Über dieses Buch

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. 

Stimmen zum Buch

“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)

Inhaltsverzeichnis (11 Kapitel)

Dieses Buch kaufen

eBook 41,64 €
Preis für Deutschland (Brutto)
  • ISBN 978-3-319-46822-8
  • Versehen mit digitalem Wasserzeichen, DRM-frei
  • Erhältliche Formate: PDF, EPUB
  • eBooks sind auf allen Endgeräten nutzbar
  • Sofortiger eBook Download nach Kauf
Softcover 53,49 €
Preis für Deutschland (Brutto)
  • ISBN 978-3-319-46821-1
  • Kostenfreier Versand für Individualkunden weltweit
  • Gewöhnlich versandfertig in 3-5 Werktagen.
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Bibliografische Information

Bibliographic Information
Buchtitel
Mod-ϕ Convergence
Buchuntertitel
Normality Zones and Precise Deviations
Autoren
Titel der Buchreihe
SpringerBriefs in Probability and Mathematical Statistics
Copyright
2016
Verlag
Springer International Publishing
Copyright Inhaber
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
Buchreihen ISSN
2365-4333
Auflage
1
Seitenzahl
XII, 152
Anzahl der Bilder und Tabellen
8 schwarz-weiß Abbildungen, 9 Abbildungen in Farbe
Themen