Percolation theory for mathematicians:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boston [u.a.]
Birkhäuser
1982
Springer Scienc, Business Media, LLC |
| Schriftenreihe: | Progress in probability and statistics
Vol. 2 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 423 Seiten Illustrationen |
| ISBN: | 3764331070 9780817631079 |
Internformat
MARC
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| 245 | 1 | 0 | |a Percolation theory for mathematicians |c Harry Kesten |
| 264 | 1 | |a Boston [u.a.] |b Birkhäuser |c 1982 | |
| 264 | 1 | |b Springer Scienc, Business Media, LLC | |
| 300 | |a 423 Seiten |b Illustrationen | ||
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| 650 | 0 | 7 | |a Statistische Physik |0 (DE-588)4057000-9 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
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| adam_text |
TABLE OF CONTENTS
1. Introduction and summary. 1
2. Which graphs do we consider? 10
2.1 Periodic graphs. 10
2.2 Matching pairs. 16
2.3 Planar modifications of matching pairs. 21
2.4 Separation theorems and related point set topological
results. 29
2.5 Covering graphs. 36
2.6 Dual graphs. 37
3. Periodic percolation problems. 40
3.1 Introduction of probability. Site vs bond problems. 40
3.2 Periodic site percolation. 44
3.3 Crossing probabilities and the principal theorem on
percolative regions. 46
3.4 Critical probabilities. Applications of the principal
theorems. 51
4. Increasing events. 69
4.1 The FKG inequality. 72
4.2 Pivotal sites and Russo's formula. 74
5. Bounds for the distribution of #W. 81
5.1 Exponential fall off of P{#W _ n). 83
5.2 Estimates above the percolation threshold. 97
5.3 Large crossing probabilities imply that percolation
occurs. 121
6. The RSW Theorem. 126
7. Proofs of Theorems 3.1 and 3.2. 168
8. Power estimates. 198
9. The nature of the singularity at p^. 238
10. Inequalities for critical probabilities. 255
10.1 Comparison of bond and site problems. 256
10.2 Strict inequality for a graph and a subgraph. 261
10.3 Derivation of Condition E from Condition D. 295
11. Resistance of random electrical networks. 335
11.1 Bounds for resistances of networks. 335
11.2 Proof of Theorem 11.1. 343
11.3 Properties of resistances. 351
11.4 Proofs of Theorems 11.2 and 11.3. 371
12. Unsolved problems. 380
Appendix. 386
References. 413
Author index. 418
Subject index. 419
Index of symbols. 421 |
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| classification_rvk | SK 170 SK 820 SK 950 |
| classification_tum | PHY 602f |
| ctrlnum | (OCoLC)230593639 (DE-599)BVBBV000194360 |
| discipline | Physik Mathematik |
| format | Book |
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| id | DE-604.BV000194360 |
| illustrated | Illustrated |
| indexdate | 2024-09-12T00:14:46Z |
| institution | BVB |
| isbn | 3764331070 9780817631079 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000113479 |
| oclc_num | 230593639 |
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| physical | 423 Seiten Illustrationen |
| psigel | TUB-www |
| publishDate | 1982 |
| publishDateSearch | 1982 |
| publishDateSort | 1982 |
| publisher | Birkhäuser Springer Scienc, Business Media, LLC |
| record_format | marc |
| series | Progress in probability and statistics |
| series2 | Progress in probability and statistics |
| spelling | Kesten, Harry 1931-2019 (DE-588)121449300 aut Percolation theory for mathematicians Harry Kesten Boston [u.a.] Birkhäuser 1982 Springer Scienc, Business Media, LLC 423 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Progress in probability and statistics Vol. 2 Perkolation (DE-588)4115530-0 gnd rswk-swf Mathematische Methode (DE-588)4155620-3 gnd rswk-swf Perkolationstheorie (DE-588)4323583-9 gnd rswk-swf Statistische Physik (DE-588)4057000-9 gnd rswk-swf Perkolationstheorie (DE-588)4323583-9 s DE-604 Perkolation (DE-588)4115530-0 s Mathematische Methode (DE-588)4155620-3 s Statistische Physik (DE-588)4057000-9 s Erscheint auch als Online-Ausgabe 978-1-4899-2730-9 Progress in probability and statistics Vol. 2 (DE-604)BV000010596 2 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000113479&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kesten, Harry 1931-2019 Percolation theory for mathematicians Progress in probability and statistics Perkolation (DE-588)4115530-0 gnd Mathematische Methode (DE-588)4155620-3 gnd Perkolationstheorie (DE-588)4323583-9 gnd Statistische Physik (DE-588)4057000-9 gnd |
| subject_GND | (DE-588)4115530-0 (DE-588)4155620-3 (DE-588)4323583-9 (DE-588)4057000-9 |
| title | Percolation theory for mathematicians |
| title_auth | Percolation theory for mathematicians |
| title_exact_search | Percolation theory for mathematicians |
| title_full | Percolation theory for mathematicians Harry Kesten |
| title_fullStr | Percolation theory for mathematicians Harry Kesten |
| title_full_unstemmed | Percolation theory for mathematicians Harry Kesten |
| title_short | Percolation theory for mathematicians |
| title_sort | percolation theory for mathematicians |
| topic | Perkolation (DE-588)4115530-0 gnd Mathematische Methode (DE-588)4155620-3 gnd Perkolationstheorie (DE-588)4323583-9 gnd Statistische Physik (DE-588)4057000-9 gnd |
| topic_facet | Perkolation Mathematische Methode Perkolationstheorie Statistische Physik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000113479&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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