Mod-ϕ Convergence: Normality Zones and Precise Deviations (SpringerBriefs in Probability and Mathematical Statistics) - Softcover

Féray, Valentin; Méliot, Pierre-Loïc; Nikeghbali, Ashkan

Softcover

ISBN 10: 3319468219 ISBN 13: 9783319468211

Publisher: Springer, 2016

Synopsis

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. 

About this title

Review

“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)

Edition details

• Publisher: Springer
• Publication date: 2016
• Language: English
• ISBN 10: 3319468219
• ISBN 13: 9783319468211
• Binding: Paperback
• Edition number: 1
• Number of pages: 164