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Mod-ϕ Convergence = Normality Zones and Precise Deviations /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Mod-ϕ Convergence/ by Valentin Féray, Pierre-Loïc Méliot, Ashkan Nikeghbali.
其他題名:	Normality Zones and Precise Deviations /
作者:	Féray, Valentin.
其他作者:	Méliot, Pierre-Loïc.
面頁冊數:	XII, 152 p. 17 illus., 9 illus. in color.online resource. :
Contained By:	Springer Nature eBook
標題:	Probabilities. -
電子資源:	https://doi.org/10.1007/978-3-319-46822-8
ISBN:	9783319468228

Mod-ϕ Convergence = Normality Zones and Precise Deviations /
Féray, Valentin.

Mod-ϕ ConvergenceNormality Zones and Precise Deviations /[electronic resource] :by Valentin Féray, Pierre-Loïc Méliot, Ashkan Nikeghbali. - 1st ed. 2016. - XII, 152 p. 17 illus., 9 illus. in color.online resource. - SpringerBriefs in Probability and Mathematical Statistics,2365-4333. - SpringerBriefs in Probability and Mathematical Statistics,.

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 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. .

ISBN: 9783319468228

Standard No.: 10.1007/978-3-319-46822-8doiSubjects--Topical Terms:

527847
Probabilities.

LC Class. No.: QA273.A1-274.9

Dewey Class. No.: 519.2

Mod-ϕ Convergence = Normality Zones and Precise Deviations /
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