Mod-ϕ Convergence Normality Zones and Precise Deviations /

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 co...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Féray, Valentin (Autor), Méliot, Pierre-Loïc (Autor), Nikeghbali, Ashkan (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Cham : Springer International Publishing : Imprint: Springer, 2016.
Edición:1st ed. 2016.
Colección:SpringerBriefs in Probability and Mathematical Statistics,
Temas:
Probabilities.
Number theory.
Discrete mathematics.
Algebras, Linear.
Probability Theory.
Number Theory.
Discrete Mathematics.
Linear Algebra.
Acceso en línea:Texto Completo
Tabla de Contenidos:
  • 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.

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