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.
Probability Theory Number Theory Combinatorics Matrix Theory Deviations
- Book Title Mod-ϕ Convergence
- Book Subtitle Normality Zones and Precise Deviations
- Series Title SpringerBriefs in Probability and Mathematical Statistics
- Series Abbreviated Title SpringerBriefs in Probabil., Math.Statist.
- 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 Mathematics and Statistics (R0)
- Softcover ISBN 978-3-319-46821-1
- eBook ISBN 978-3-319-46822-8
- Series ISSN 2365-4333
- Series E-ISSN 2365-4341
- Edition Number 1
- Number of Pages XII, 152
- Number of Illustrations 8 b/w illustrations, 9 illustrations in colour
Probability Theory and Stochastic Processes
Linear and Multilinear Algebras, Matrix Theory
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“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)