Mod-ϕ Convergence Normality Zones and Precise Deviations /

• Κύριοι συγγραφείς: Féray, Valentin (Συγγραφέας), Méliot, Pierre-Loïc (Συγγραφέας), Nikeghbali, Ashkan (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Cham : Springer International Publishing : Imprint: Springer, 2016.
• Σειρά: SpringerBriefs in Probability and Mathematical Statistics,
• Θέματα: 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...

Πίνακας περιεχομένων:

• 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.