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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...
| Clasificación: | Libro Electrónico |
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| Autores principales: | , , |
| Autor Corporativo: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cham :
Springer International Publishing : Imprint: Springer,
2016.
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| Edición: | 1st ed. 2016. |
| Colección: | SpringerBriefs in Probability and Mathematical Statistics,
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| Temas: | |
| Acceso en línea: | Texto Completo |
MARC
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| 001 | 978-3-319-46822-8 | ||
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| 024 | 7 | |a 10.1007/978-3-319-46822-8 |2 doi | |
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| 100 | 1 | |a Féray, Valentin. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 0 | |a Mod-ϕ Convergence |h [electronic resource] : |b Normality Zones and Precise Deviations / |c by Valentin Féray, Pierre-Loïc Méliot, Ashkan Nikeghbali. |
| 250 | |a 1st ed. 2016. | ||
| 264 | 1 | |a Cham : |b Springer International Publishing : |b Imprint: Springer, |c 2016. | |
| 300 | |a XII, 152 p. 17 illus., 9 illus. in color. |b online resource. | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
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| 347 | |a text file |b PDF |2 rda | ||
| 490 | 1 | |a SpringerBriefs in Probability and Mathematical Statistics, |x 2365-4341 | |
| 505 | 0 | |a 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. | |
| 520 | |a 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. . | ||
| 650 | 0 | |a Probabilities. | |
| 650 | 0 | |a Number theory. | |
| 650 | 0 | |a Discrete mathematics. | |
| 650 | 0 | |a Algebras, Linear. | |
| 650 | 1 | 4 | |a Probability Theory. |
| 650 | 2 | 4 | |a Number Theory. |
| 650 | 2 | 4 | |a Discrete Mathematics. |
| 650 | 2 | 4 | |a Linear Algebra. |
| 700 | 1 | |a Méliot, Pierre-Loïc. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 700 | 1 | |a Nikeghbali, Ashkan. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 710 | 2 | |a SpringerLink (Online service) | |
| 773 | 0 | |t Springer Nature eBook | |
| 776 | 0 | 8 | |i Printed edition: |z 9783319468211 |
| 776 | 0 | 8 | |i Printed edition: |z 9783319468235 |
| 830 | 0 | |a SpringerBriefs in Probability and Mathematical Statistics, |x 2365-4341 | |
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| 950 | |a Mathematics and Statistics (SpringerNature-11649) | ||
| 950 | |a Mathematics and Statistics (R0) (SpringerNature-43713) | ||