Continuum percolation:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge University Press
[1996]
|
| Ausgabe: | First published |
| Schriftenreihe: | Cambridge tracts in mathematics
119 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | x, 238 Seiten Illustrationen |
| ISBN: | 052147504X |
Internformat
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| 245 | 1 | 0 | |a Continuum percolation |c Ronald Meester ; Rahul Roy |
| 250 | |a First published | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge University Press |c [1996] | |
| 264 | 4 | |c © 1996 | |
| 300 | |a x, 238 Seiten |b Illustrationen | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Cambridge tracts in mathematics |v 119 | |
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Datensatz im Suchindex
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| adam_text |
Contents
Preface page ix
1 Introduction 1
1.1 Motivation for continuum models 1
1.2 Discrete percolation 2
1.3 Stationary point processes 9
1.4 The Boolean model 14
1.5 The random connection model 18
1.6 Notes 20
2 Basic methods 21
2.1 Ergodicity 21
2.2 Coupling and scaling 28
2.3 The FKG inequality 31
2.4 The BK inequality 34
2.5 Notes 39
3 Occupancy in Poisson Boolean models 40
3.1 Introduction 40
3.2 One dimensional triviality 43
3.3 Critical phenomena 45
3.4 Critical densities 52
3.5 Equality of the critical densities 59
3.6 Uniqueness 63
3.7 Exponential decay 68
3.8 Continuity of the critical density and the percolation function 71
v
vi Contents
3.9 Bounds on Xc and asymptotics for the cluster size 85
3.10 Notes 90
4 Vacancy in Poisson Boolean models 91
4.1 Critical densities 92
4.2 RSW notation and definition 95
4.3 RSW construction 97
4.4 RSW preliminary results 103
4.5 RSW proof 106
4.6 Equality of the critical densities 108
4.7 Uniqueness 116
4.8 Continuity of the percolation function 119
4.9 Notes 121
5 Distinguishing features of the Poisson Boolean model 122
5.1 The covered volume fraction 122
5.2 Compression 125
5.3 Rarefaction 138
5.4 Notes 150
6 The Poisson random connection model 151
6.1 Non triviality of the model 152
6.2 Properties of the connection function 155
6.3 Equality of the critical densities 159
6.4 Uniqueness 172
6.5 High density 173
6.6 Notes 180
7 Models driven by general processes 181
7.1 Ergodic decomposition 181
7.2 Basic facts on coverage 184
7.3 Unbounded components in Boolean models 187
7.4 Uniqueness in Boolean models 194
7.5 Uniqueness in random connection models 197
7.6 Cutting and stacking 199
7.7 Examples 204
7.8 Notes 208
Contents vii
8 Other continuum percolation models 209
8.1 Continuum fractal percolation 209
8.2 Percolation of level sets in random fields 216
8.3 Dependent Boolean and random connection models 221
8.4 Stationary spanning forests 226
8.5 Percolation of Poisson sticks 229
8.6 Notes 232
References 233
Index 237 |
| any_adam_object | 1 |
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| id | DE-604.BV011030691 |
| illustrated | Illustrated |
| indexdate | 2024-11-06T11:02:00Z |
| institution | BVB |
| isbn | 052147504X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007386199 |
| oclc_num | 231687131 |
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| physical | x, 238 Seiten Illustrationen |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Cambridge University Press |
| record_format | marc |
| series | Cambridge tracts in mathematics |
| series2 | Cambridge tracts in mathematics |
| spelling | Meester, Ronaldus W. 1963- (DE-588)172254019 aut Continuum percolation Ronald Meester ; Rahul Roy First published Cambridge [u.a.] Cambridge University Press [1996] © 1996 x, 238 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Cambridge tracts in mathematics 119 Perkolation (DE-588)4115530-0 gnd rswk-swf Perkolation (DE-588)4115530-0 s DE-604 Roy, Rahul (DE-588)170929159 aut Erscheint auch als Online-Ausgabe 978-0-511-89535-7 Cambridge tracts in mathematics 119 (DE-604)BV000000001 119 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007386199&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Meester, Ronaldus W. 1963- Roy, Rahul Continuum percolation Cambridge tracts in mathematics Perkolation (DE-588)4115530-0 gnd |
| subject_GND | (DE-588)4115530-0 |
| title | Continuum percolation |
| title_auth | Continuum percolation |
| title_exact_search | Continuum percolation |
| title_full | Continuum percolation Ronald Meester ; Rahul Roy |
| title_fullStr | Continuum percolation Ronald Meester ; Rahul Roy |
| title_full_unstemmed | Continuum percolation Ronald Meester ; Rahul Roy |
| title_short | Continuum percolation |
| title_sort | continuum percolation |
| topic | Perkolation (DE-588)4115530-0 gnd |
| topic_facet | Perkolation |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007386199&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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