Mod-ϕ Convergence

Normality Zones and Precise Deviations

Häftad, Engelska, 2016

Av Valentin Féray, Pierre-Loïc Méliot, Ashkan Nikeghbali, Valentin Feray, Pierre-Loic Meliot, Ashkan Méliot, Pierre-Loïc

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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.

Produktinformation

Utgivningsdatum2016-12-16
Mått155 x 235 x 14 mm
Vikt268 g
FormatHäftad
SpråkEngelska
SerieSpringerBriefs in Probability and Mathematical Statistics
Antal sidor152
FörlagSpringer International Publishing AG
ISBN9783319468211

Tillhör följande kategorier

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.

“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)