Mod-ϕ Convergence Normality Zones and Precise Deviations /

• Main Authors: Féray, Valentin (Author), Méliot, Pierre-Loïc (Author), Nikeghbali, Ashkan (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2016.
• Series: SpringerBriefs in Probability and Mathematical Statistics,
• Subjects: Mathematics.; Matrix theory.; Algebra.; Number theory.; Probabilities.; Combinatorics.; Probability Theory and Stochastic Processes.; Number Theory.; Linear and Multilinear Algebras, Matrix Theory.

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 converge...

Table of 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.