Logarithmic combinatorial structures: a probabilistic approach:
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | German |
| Veröffentlicht: |
Zürich
European Mathematical Society
2003
|
| Schriftenreihe: | EMS monographs in mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XI, 363 Seiten graph. Darst. |
| ISBN: | 3037190000 |
Internformat
MARC
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| 100 | 1 | |a Arratia, Richard |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Logarithmic combinatorial structures: a probabilistic approach |c Richard Arratia ; A. D. Barbour ; Simon Tavaré |
| 264 | 1 | |a Zürich |b European Mathematical Society |c 2003 | |
| 300 | |a XI, 363 Seiten |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a EMS monographs in mathematics | |
| 650 | 7 | |a Combinatieleer |2 gtt | |
| 650 | 4 | |a Distribution asymptotique (Théorie des probabilités) | |
| 650 | 7 | |a Distribution asymptotique (Théorie des probabilités) |2 rasuqam | |
| 650 | 7 | |a Développement asymptotique |2 rasuqam | |
| 650 | 4 | |a Développements asymptotiques | |
| 650 | 7 | |a Probabilité combinatoire |2 rasuqam | |
| 650 | 4 | |a Probabilités combinatoires | |
| 650 | 7 | |a Processus stochastique |2 rasuqam | |
| 650 | 4 | |a Processus stochastiques | |
| 650 | 7 | |a Waarschijnlijkheidstheorie |2 gtt | |
| 650 | 4 | |a Asymptotic distribution (Probability theory) | |
| 650 | 4 | |a Asymptotic expansions | |
| 650 | 4 | |a Combinatorial probabilities | |
| 650 | 4 | |a Stochastic processes | |
| 650 | 0 | 7 | |a Kombinatorische Wahrscheinlichkeitstheorie |0 (DE-588)4132446-8 |2 gnd |9 rswk-swf |
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| 700 | 1 | |a Barbour, Andrew D. |e Verfasser |4 aut | |
| 700 | 1 | |a Tavaré, Simon |e Verfasser |4 aut | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-012815829 | ||
Datensatz im Suchindex
| _version_ | 1804132781906722816 |
|---|---|
| adam_text | Contents
0 Preface 1
1 Permutations and Primes
1.1 Random permutations and their cycles 9
1.2 Random integers and their prime factors 27
1.3 Contrasts between permutations and primes 32
2 Decomposable Combinatorial Structures
2.1 Some combinatorial examples 36
2.2 Assemblies, multisets and selections 45
2.3 The probabilistic perspective 48
2.4 Refining and coloring 53
2.5 Tilting 58
3 Probabilistic Preliminaries
3.1 Total variation and Wasserstein distances 67
3.2 Rates of convergence 68
3.3 Results for classical logarithmic structures 70
3.4 Stein s method 73
4 The Ewens Sampling Formula: Methods
4.1 Size biasing 78
4.2 The limiting random variable Xe 80
4.3 The limiting random variable Xe 85
4.4 Point probabilities for T(,n 89
5 The Ewens Sampling Formula: Asymptotics
5.1 Weak laws for small cycles 96
5.2 The number of cycles 100
5.3 The shortest cycles 104
5.4 The ordered cycles 106
x Contents
5.5 The largest cycles 108
5.6 The Erdos Turan Law 115
5.7 The Poisson Dirichlet and GEM distributions 117
6 Logarithmic Combinatorial Structures
6.1 Results for general logarithmic structures 125
6.2 Verifying the local limit conditions 138
6.3 Refinements and extensions 147
7 General Setting
7.1 Strategy 149
7.2 Basic framework 153
7.3 Working conditions 155
7.4 Tilting 160
7.5 d fractions 163
7.6 Illustrations 164
7.7 Main theorems 165
8 Consequences
8.1 Functional central limit theorems 171
8.2 Poisson Dirichlet limits 175
8.3 The number of components 186
8.4 Erdos Turan laws 199
8.5 Additive function theory 200
9 A Stein Equation
9.1 Stein s method for TOm(Z*) 225
9.2 Stein s method for Pe 230
9.3 Applying Stein s method 234
10 Point Probabilities
10.1 Bounds on individual probabilities 239
10.2 Differences of point probabilities 247
11 Distributional Comparisons with P$
11.1 Comparison of C(Tvm(Z)) and C(Tvm(Z*)) 267
11.2 Comparing C(m~xTvm{Z*)) with Pe 277
11.3 Comparing C{mrlTvm(Z*)) with PJq) 282
12 Comparisons with Pe: Point Probabilities
12.1 Local limit theorems for Tvm(Z) 285
12.2 Comparison of Tvm(Z) with Tvm(Z*): point probabilities 288
12.3 Comparison with pe 297
Contents xi
13 Proofs
13.1 Proof of Theorem 7.(j 301
13.2 Proof of Theorem 7.7 302
13.3 Proof of Theorem 7.8 304
13.4 Proof of Theorem 7.9 307
13.5 Proof of Theorem 7.10 310
13.6 Proof of Theorem 7.11 312
13.7 Proof of Theorem 7.12 313
13.8 Proof of Theorem 7.13 314
13.9 Proof of Theorem 7.14 319
13.10 Proof of Theorem 8.10 323
14 Technical Complements 329
References 339
Notation Index 353
Author Index 355
Subject Index 359
|
| any_adam_object | 1 |
| author | Arratia, Richard Barbour, Andrew D. Tavaré, Simon |
| author_facet | Arratia, Richard Barbour, Andrew D. Tavaré, Simon |
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| classification_tum | MAT 602f |
| ctrlnum | (OCoLC)54504695 (DE-599)BVBBV019351776 |
| dewey-full | 519.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2 |
| dewey-search | 519.2 |
| dewey-sort | 3519.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV019351776 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T19:58:17Z |
| institution | BVB |
| isbn | 3037190000 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-012815829 |
| oclc_num | 54504695 |
| open_access_boolean | |
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| physical | XI, 363 Seiten graph. Darst. |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | European Mathematical Society |
| record_format | marc |
| series2 | EMS monographs in mathematics |
| spelling | Arratia, Richard Verfasser aut Logarithmic combinatorial structures: a probabilistic approach Richard Arratia ; A. D. Barbour ; Simon Tavaré Zürich European Mathematical Society 2003 XI, 363 Seiten graph. Darst. txt rdacontent n rdamedia nc rdacarrier EMS monographs in mathematics Combinatieleer gtt Distribution asymptotique (Théorie des probabilités) Distribution asymptotique (Théorie des probabilités) rasuqam Développement asymptotique rasuqam Développements asymptotiques Probabilité combinatoire rasuqam Probabilités combinatoires Processus stochastique rasuqam Processus stochastiques Waarschijnlijkheidstheorie gtt Asymptotic distribution (Probability theory) Asymptotic expansions Combinatorial probabilities Stochastic processes Kombinatorische Wahrscheinlichkeitstheorie (DE-588)4132446-8 gnd rswk-swf Kombinatorische Wahrscheinlichkeitstheorie (DE-588)4132446-8 s DE-604 Barbour, Andrew D. Verfasser aut Tavaré, Simon Verfasser aut Erscheint auch als Online-Ausgabe 978-3-03719-000-5 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012815829&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Arratia, Richard Barbour, Andrew D. Tavaré, Simon Logarithmic combinatorial structures: a probabilistic approach Combinatieleer gtt Distribution asymptotique (Théorie des probabilités) Distribution asymptotique (Théorie des probabilités) rasuqam Développement asymptotique rasuqam Développements asymptotiques Probabilité combinatoire rasuqam Probabilités combinatoires Processus stochastique rasuqam Processus stochastiques Waarschijnlijkheidstheorie gtt Asymptotic distribution (Probability theory) Asymptotic expansions Combinatorial probabilities Stochastic processes Kombinatorische Wahrscheinlichkeitstheorie (DE-588)4132446-8 gnd |
| subject_GND | (DE-588)4132446-8 |
| title | Logarithmic combinatorial structures: a probabilistic approach |
| title_auth | Logarithmic combinatorial structures: a probabilistic approach |
| title_exact_search | Logarithmic combinatorial structures: a probabilistic approach |
| title_full | Logarithmic combinatorial structures: a probabilistic approach Richard Arratia ; A. D. Barbour ; Simon Tavaré |
| title_fullStr | Logarithmic combinatorial structures: a probabilistic approach Richard Arratia ; A. D. Barbour ; Simon Tavaré |
| title_full_unstemmed | Logarithmic combinatorial structures: a probabilistic approach Richard Arratia ; A. D. Barbour ; Simon Tavaré |
| title_short | Logarithmic combinatorial structures: a probabilistic approach |
| title_sort | logarithmic combinatorial structures a probabilistic approach |
| topic | Combinatieleer gtt Distribution asymptotique (Théorie des probabilités) Distribution asymptotique (Théorie des probabilités) rasuqam Développement asymptotique rasuqam Développements asymptotiques Probabilité combinatoire rasuqam Probabilités combinatoires Processus stochastique rasuqam Processus stochastiques Waarschijnlijkheidstheorie gtt Asymptotic distribution (Probability theory) Asymptotic expansions Combinatorial probabilities Stochastic processes Kombinatorische Wahrscheinlichkeitstheorie (DE-588)4132446-8 gnd |
| topic_facet | Combinatieleer Distribution asymptotique (Théorie des probabilités) Développement asymptotique Développements asymptotiques Probabilité combinatoire Probabilités combinatoires Processus stochastique Processus stochastiques Waarschijnlijkheidstheorie Asymptotic distribution (Probability theory) Asymptotic expansions Combinatorial probabilities Stochastic processes Kombinatorische Wahrscheinlichkeitstheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012815829&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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