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Mod-ϕ convergence : normality zones and precise deviations / by Valentin Féray, Pierre-Loïc Méliot, Ashkan Nikeghbali.
Springer Nature - Springer Mathematics and Statistics eBooks 2016 English International Available online
View online- Format:
- Book
- Author/Creator:
- Féray, Valentin, Author.
- Méliot, Pierre-Loic, 1985- Author.
- Nikeghbali, Ashkan, 1975- Author.
- Series:
- SpringerBriefs in Probability and Mathematical Statistics, 2365-4333
- Language:
- English
- Subjects (All):
- Probabilities.
- Number theory.
- Combinatorial analysis.
- Matrix theory.
- Algebra.
- Probability Theory and Stochastic Processes.
- Number Theory.
- Combinatorics.
- Linear and Multilinear Algebras, Matrix Theory.
- Local Subjects:
- Probability Theory and Stochastic Processes.
- Number Theory.
- Combinatorics.
- Linear and Multilinear Algebras, Matrix Theory.
- Physical Description:
- 1 online resource (XII, 152 p. 17 illus., 9 illus. in color.)
- Edition:
- 1st ed. 2016.
- Place of Publication:
- Cham : Springer International Publishing : Imprint: Springer, 2016.
- Summary:
- 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. .
- Contents:
- Preface
- Introduction
- Preliminaries
- Fluctuations in the case of lattice distributions
- Fluctuations in the non-lattice case
- An extended deviation result from bounds on cumulants
- A precise version of the Ellis-Gärtner theorem
- Examples with an explicit generating function
- Mod-Gaussian convergence from a factorisation of the PGF
- Dependency graphs and mod-Gaussian convergence
- Subgraph count statistics in Erdös-Rényi random graphs
- Random character values from central measures on partitions
- Bibliography.
- Notes:
- Includes bibliographical references.
- ISBN:
- 3-319-46822-7
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