Mod-ϕ Convergence: normality zones and precise deviations
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cham
Springer
[2016]
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| Schriftenreihe: | Springer Briefs in probability and mathematical statistics
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xii, 152 Seiten Illustrationen, Diagramme |
| ISBN: | 9783319468211 |
Internformat
MARC
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Datensatz im Suchindex
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| adam_text | Contents Preface Acknowledgements Chapter 1. Introduction 1.1. Mod-ф convergence 1.2. Theoretical results 1.3. Applications 1.4. Forthcoming works 1.5. Discussion on our hypotheses vii ix 1 1 3 5 7 7 Chapter 2. Preliminaries 2.1. Basic examples of mod-convergence 2.2. Legendre-Fenchel transforms 2.3. Gaussian integrals 9 9 13 14 Chapter 3. Fluctuations in the case of lattice distributions 3.1. Lattice and non-lattice distributions 3.2. Deviations at the scale O(rn) 3.3. Central limit theorem at the scales o(t„) and օ((էռ)2^3) 17 17 20 26 Chapter 4. Fluctuations in the non-lattice case 4.1. Berry-Esseen estimates 4.2. Deviations at scale O(tn) 4.3. Central limit theorem at the scales o(tn) and о((ѓп)2//3) 4.4. Normality zones for mod-ф and mod-Gaussian sequences 4.5. Discussion and refinements 33 33 37 40 46 48 Chapter 5. An extended deviation result from bounds on cumulants 5.1. Bounds on cumulants and mod-Gaussian convergence 5.2. Precise deviations for random variables with control on cumulants 5.3. Link with the Cramér-Petrov expansion 51 51 52 57 Chapter 6. A precise version of the Ellis-Gärtner theorem 6.1. Technical preliminaries 6.2. A precise upper bound 6.3. A precise lower bound 59 60 61 62 xi
xii CONTENTS Chapter 7. Examples with an explicit generating function 7.1. Mod-convergence from an explicit formula for the Laplace transform 7.2. Additive arithmetic functions of random integers 7.3. Number of cycles in weighted probability measure 7.4. Rises in random permutations 7.5. Characteristic polynomials of random matrices in a compact Lie group 65 65 68 74 79 82 Chapter 8. Mod-Gaussian convergence from a factorisation of the PGF 8.1. Background: central limit theorem from location of zeros 8.2. Mod-Gaussian convergence from non-negative factorisations 8.3. Two examples: uniform permutations and uniform set-partitions 8.4. Third cumulant of the number of blocks in uniform set-partitions 87 87 88 91 93 Chapter 9. Dependency graphs and mod-Gaussian convergence 9.1. The theory of dependency graphs 9.2. Joint cumulants 9.3. Useful combinatorial lemmas 9.4. Proof of the bound on cumulants 9.5. Sums of random variables with a sparse dependency graph 95 97 99 101 106 109 Chapter 10. Subgraph count statistics in Erdös-Rényi random graphs 10.1. A bound on cumulants 10.2. Polynomiality of cumulants 10.3. Moderate deviations for subgraph count statistics 111 113 115 117 Chapter 11. Random character values from central measures on partitions 11.1. Background 11.2. Definitions and results 11.3. Technical preliminaries 11.4. Bounds and limits of the cumulants 11.5. Asymptotics of the random charactervalues and partitions 123 123 124 128 131 136 Bibliography 141
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| dewey-sort | 3519.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV044232852 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T07:47:17Z |
| institution | BVB |
| isbn | 9783319468211 |
| language | English |
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| spelling | Féray, Valentin 1984- (DE-588)1132227054 aut Mod-ϕ Convergence normality zones and precise deviations Valentin Féray, Pierre-Loïc Méliot, Ashkan Nikeghbali mod Cham Springer [2016] © 2016 xii, 152 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Springer Briefs in probability and mathematical statistics Mathematics Matrix theory Algebra Number theory Probabilities Combinatorics Probability Theory and Stochastic Processes Number Theory Linear and Multilinear Algebras, Matrix Theory Mathematik Konvergenz (DE-588)4032326-2 gnd rswk-swf Zufallsvariable (DE-588)4129514-6 gnd rswk-swf Zufallsvariable (DE-588)4129514-6 s Konvergenz (DE-588)4032326-2 s DE-604 Méliot, Pierre-Loïc 1985- (DE-588)1128914883 aut Nikeghbali, Ashkan 1975- (DE-588)1054746265 aut Erscheint auch als Online-Ausgabe 978-3-319-46822-8 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029638443&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Féray, Valentin 1984- Méliot, Pierre-Loïc 1985- Nikeghbali, Ashkan 1975- Mod-ϕ Convergence normality zones and precise deviations Mathematics Matrix theory Algebra Number theory Probabilities Combinatorics Probability Theory and Stochastic Processes Number Theory Linear and Multilinear Algebras, Matrix Theory Mathematik Konvergenz (DE-588)4032326-2 gnd Zufallsvariable (DE-588)4129514-6 gnd |
| subject_GND | (DE-588)4032326-2 (DE-588)4129514-6 |
| title | Mod-ϕ Convergence normality zones and precise deviations |
| title_alt | mod |
| title_auth | Mod-ϕ Convergence normality zones and precise deviations |
| title_exact_search | Mod-ϕ Convergence normality zones and precise deviations |
| title_full | Mod-ϕ Convergence normality zones and precise deviations Valentin Féray, Pierre-Loïc Méliot, Ashkan Nikeghbali |
| title_fullStr | Mod-ϕ Convergence normality zones and precise deviations Valentin Féray, Pierre-Loïc Méliot, Ashkan Nikeghbali |
| title_full_unstemmed | Mod-ϕ Convergence normality zones and precise deviations Valentin Féray, Pierre-Loïc Méliot, Ashkan Nikeghbali |
| title_short | Mod-ϕ Convergence |
| title_sort | mod ϕ convergence normality zones and precise deviations |
| title_sub | normality zones and precise deviations |
| topic | Mathematics Matrix theory Algebra Number theory Probabilities Combinatorics Probability Theory and Stochastic Processes Number Theory Linear and Multilinear Algebras, Matrix Theory Mathematik Konvergenz (DE-588)4032326-2 gnd Zufallsvariable (DE-588)4129514-6 gnd |
| topic_facet | Mathematics Matrix theory Algebra Number theory Probabilities Combinatorics Probability Theory and Stochastic Processes Number Theory Linear and Multilinear Algebras, Matrix Theory Mathematik Konvergenz Zufallsvariable |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029638443&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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