Percolation:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2006
|
| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 323 S. Ill., graph. Darst. |
| ISBN: | 0521872324 9780521872324 |
Staff View
MARC
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Record in the Search Index
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| adam_text | Contents Preface page ix 1 Basic concepts and results 2 Probabilistic tools 36 3 Bond percolation on Z2 ֊ the Harris—Kesten Theorem 3.1 The Russo-Seymour-Welsh method 3.2 Harris’s Theorem 3.3 A sharp transition 3.4 Kesten’s Theorem 3.5 Dependent percolation and exponential decay 3.6 Sub-exponential decay 50 57 61 63 67 70 76 4 Exponential decay and critical probabilities — theo rems of Menshikov and Aizenman Barsky 78 4.1 The van den Berg-Kesten inequality and percolation 78 4.2 Oriented site percolation 80 4.3 Almost exponential decay of the radius - Menshikov’s Theorem 90 4.4 Exponential decay of the radius 104 4.5 Exponential decay of the volume - the AizenmanNewman Theorem 107 5 Uniqueness of the infinite open cluster and critical probabilities 117 5.1 Uniqueness of the infinite open cluster - the Aizenman-Kesten-Newman Theorem 117 5.2 The Harris-Kesten Theorem revisited 124 5.3 Site percolation on the triangular andsquare lattices 129 5.4 Bond percolation on a lattice and its dual 136 vii 1
Contents viii The star-delta transformation 148 Estimating critical probabilities 156 156 162 167 175 5.5 6 6.1 6.2 6.3 6.4 7 Conformal invariance — Smirnov’s Theorem 7.1 7.2 7.3 8 The substitution method Comparison with dependent percolation Oriented percolation on Z2 Non-rigorous bounds Crossing probabilities and conformalinvariance Smirnov’s Theorem Critical exponents and Schramm-Loewner evolution Continuum percolation 8.1 The Gilbert disc model 8.2 Finite random geometric graphs 8.3 Random Voronoi percolation Bibliography Index List of notation 178 178 187 232 240 241 254 263 299 319 322
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| adam_txt |
Contents Preface page ix 1 Basic concepts and results 2 Probabilistic tools 36 3 Bond percolation on Z2 ֊ the Harris—Kesten Theorem 3.1 The Russo-Seymour-Welsh method 3.2 Harris’s Theorem 3.3 A sharp transition 3.4 Kesten’s Theorem 3.5 Dependent percolation and exponential decay 3.6 Sub-exponential decay 50 57 61 63 67 70 76 4 Exponential decay and critical probabilities — theo rems of Menshikov and Aizenman Barsky 78 4.1 The van den Berg-Kesten inequality and percolation 78 4.2 Oriented site percolation 80 4.3 Almost exponential decay of the radius - Menshikov’s Theorem 90 4.4 Exponential decay of the radius 104 4.5 Exponential decay of the volume - the AizenmanNewman Theorem 107 5 Uniqueness of the infinite open cluster and critical probabilities 117 5.1 Uniqueness of the infinite open cluster - the Aizenman-Kesten-Newman Theorem 117 5.2 The Harris-Kesten Theorem revisited 124 5.3 Site percolation on the triangular andsquare lattices 129 5.4 Bond percolation on a lattice and its dual 136 vii 1
Contents viii The star-delta transformation 148 Estimating critical probabilities 156 156 162 167 175 5.5 6 6.1 6.2 6.3 6.4 7 Conformal invariance — Smirnov’s Theorem 7.1 7.2 7.3 8 The substitution method Comparison with dependent percolation Oriented percolation on Z2 Non-rigorous bounds Crossing probabilities and conformalinvariance Smirnov’s Theorem Critical exponents and Schramm-Loewner evolution Continuum percolation 8.1 The Gilbert disc model 8.2 Finite random geometric graphs 8.3 Random Voronoi percolation Bibliography Index List of notation 178 178 187 232 240 241 254 263 299 319 322 |
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| discipline | Physik Mathematik |
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| edition | 1. publ. |
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| illustrated | Illustrated |
| index_date | 2024-07-02T15:59:27Z |
| indexdate | 2024-07-09T20:45:48Z |
| institution | BVB |
| isbn | 0521872324 9780521872324 |
| language | English |
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| physical | X, 323 S. Ill., graph. Darst. |
| publishDate | 2006 |
| publishDateSearch | 2006 |
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| publisher | Cambridge Univ. Press |
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| spelling | Bollobás, Béla 1943- Verfasser (DE-588)109481240 aut Percolation Béla Bollobás ; Oliver Riordan 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2006 X, 323 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Perkolation Perkolationstheorie Percolation (Statistical physics) Perkolationstheorie (DE-588)4323583-9 gnd rswk-swf Perkolation (DE-588)4115530-0 gnd rswk-swf Perkolation (DE-588)4115530-0 s DE-604 Perkolationstheorie (DE-588)4323583-9 s Riordan, Oliver Sonstige (DE-588)120930102 oth 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=015050032&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bollobás, Béla 1943- Percolation Perkolation Perkolationstheorie Percolation (Statistical physics) Perkolationstheorie (DE-588)4323583-9 gnd Perkolation (DE-588)4115530-0 gnd |
| subject_GND | (DE-588)4323583-9 (DE-588)4115530-0 |
| title | Percolation |
| title_auth | Percolation |
| title_exact_search | Percolation |
| title_exact_search_txtP | Percolation |
| title_full | Percolation Béla Bollobás ; Oliver Riordan |
| title_fullStr | Percolation Béla Bollobás ; Oliver Riordan |
| title_full_unstemmed | Percolation Béla Bollobás ; Oliver Riordan |
| title_short | Percolation |
| title_sort | percolation |
| topic | Perkolation Perkolationstheorie Percolation (Statistical physics) Perkolationstheorie (DE-588)4323583-9 gnd Perkolation (DE-588)4115530-0 gnd |
| topic_facet | Perkolation Perkolationstheorie Percolation (Statistical physics) |
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