Verfügbarkeit: Percolation | Technische Universität München

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Bibliographische Detailangaben
Beteilige Person:	Grimmett, Geoffrey 1950- (VerfasserIn)
Format:	Buch
Sprache:	Deutsch
Veröffentlicht:	Berlin ; Heidelberg Springer [1999]
Ausgabe:	second edition
Schriftenreihe:	Grundlehren der mathematischen Wissenschaften 321
Schlagwörter:	Perkolation Perkolationstheorie Statistische Physik
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008489689&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Umfang:	xiii, 444 Seiten Illustrationen
ISBN:	3540649026 9783642084423 9783540649021

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adam_text	Contents 1 What is Percolation? 1 1.1 Modelling a Random Medium 1 1.2 Why Percolation? 3 1.3 Bond Percolation 9 1.4 The Critical Phenomenon 13 1.5 The Main Questions 20 1.6 Site Percolation 24 1.7 Notes 29 2 Some Basic Techniques 32 2.1 Increasing Events 32 2.2 The FKG Inequality 34 2.3 The BK Inequality 37 2.4 Russo's Formula 41 2.5 Inequalities of Reliability Theory 46 2.6 Another Inequality 49 2.7 Notes 51 3 Critical Probabilities 53 3.1 Equalities and Inequalities 53 3.2 Strict Inequalities 57 3.3 Enhancements 63 3.4 Bond and Site Critical Probabilities 71 3.5 Notes 75 4 The Number of Open Clusters per Vertex 77 4.1 Definition 77 4.2 Lattice Animals and Large Deviations 79 4.3 Differentiability of k 84 4.4 Notes 86 xii Contents 5 Exponential Decay 87 5.1 Mean Cluster Size 87 5.2 Exponential Decay of the Radius Distribution beneath pc 88 5.3 Using Differential Inequalities 102 5.4 Notes 114 6 The Subcritical Phase 117 6.1 The Radius of an Open Cluster 117 6.2 Connectivity Functions and Correlation Length 126 6.3 Exponential Decay of the Cluster Size Distribution 132 6.4 Analyticity of k and x 142 6.5 Notes 144 7 Dynamic and Static Renormalization 146 7.1 Percolation in Slabs 146 7.2 Percolation of Blocks 148 7.3 Percolation in Half Spaces 162 7.4 Static Renormalization 176 7.5 Notes 196 8 The Supercritical Phase 197 8.1 Introduction 197 8.2 Uniqueness of the Infinite Open Cluster 198 8.3 Continuity of the Percolation Probability 202 8.4 The Radius of a Finite Open Cluster 205 8.5 Truncated Connectivity Functions and Correlation Length 213 8.6 Sub Exponential Decay of the Cluster Size Distribution 215 8.7 Differentiability of 6, /f, and k 224 8.8 Geometry of the Infinite Open Cluster 226 8.9 Notes 229 9 Near the Critical Point: Scaling Theory 232 9.1 Power Laws and Critical Exponents 232 9.2 Scaling Theory 239 9.3 Renormalization 244 9.4 The Incipient Infinite Cluster 249 9.5 Notes 252 10 Near the Critical Point: Rigorous Results 254 10.1 Percolation on a Tree 254 10.2 Inequalities for Critical Exponents 262 10.3 Mean Field Theory 269 10.4 Notes 278 Contents xiii 11 Bond Percolation in Two Dimensions 281 11.1 Introduction 281 11.2 Planar Duality 283 11.3 The Critical Probability Equals \ 287 11.4 Tail Estimates in the Supercritical Phase 295 11.5 Percolation on Subsets of the Square Lattice 303 11.6 Central Limit Theorems 309 11.7 Open Circuits in Annuli 314 11.8 Power Law Inequalities 324 11.9 Inhomogeneous Square and Triangular Lattices 331 11.10 Notes 345 12 Extensions of Percolation 349 12.1 Mixed Percolation on a General Lattice 349 12.2 AB Percolation 351 12.3 Long Range Percolation in One Dimension 351 12.4 Surfaces in Three Dimensions 359 12.5 Entanglement in Percolation 362 12.6 Rigidity in Percolation 364 12.7 Invasion Percolation 366 12.8 Oriented Percolation 367 12.9 First Passage Percolation 369 12.10 Continuum Percolation 371 13 Percolative Systems 378 13.1 Capacitated Networks 378 13.2 Random Electrical Networks 380 13.3 Stochastic Pin Ball 382 13.4 Fractal Percolation 385 13.5 Contact Model 390 13.6 Random Cluster Model 393 Appendix I. The Infinite Volume Limit for Percolation 397 Appendix II. The Subadditive Inequality 399 List of Notation 401 References 404 Index of Names 435 Subject Index 439
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author	Grimmett, Geoffrey 1950-
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dewey-raw	530.13
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discipline	Physik Mathematik
edition	second edition
format	Book
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illustrated	Illustrated
indexdate	2025-01-14T05:15:37Z
institution	BVB
isbn	3540649026 9783642084423 9783540649021
language	German
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-008489689
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owner	DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-384 DE-20 DE-824 DE-29 DE-29T DE-703 DE-706 DE-634 DE-83 DE-11 DE-188
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physical	xiii, 444 Seiten Illustrationen
publishDate	1999
publishDateSearch	1999
publishDateSort	1999
publisher	Springer
record_format	marc
series	Grundlehren der mathematischen Wissenschaften
series2	Grundlehren der mathematischen Wissenschaften
spellingShingle	Grimmett, Geoffrey 1950- Percolation Grundlehren der mathematischen Wissenschaften Perkolation (DE-588)4115530-0 gnd Perkolationstheorie (DE-588)4323583-9 gnd Statistische Physik (DE-588)4057000-9 gnd
subject_GND	(DE-588)4115530-0 (DE-588)4323583-9 (DE-588)4057000-9
title	Percolation
title_auth	Percolation
title_exact_search	Percolation
title_full	Percolation Geoffrey Grimmett
title_fullStr	Percolation Geoffrey Grimmett
title_full_unstemmed	Percolation Geoffrey Grimmett
title_short	Percolation
title_sort	percolation
topic	Perkolation (DE-588)4115530-0 gnd Perkolationstheorie (DE-588)4323583-9 gnd Statistische Physik (DE-588)4057000-9 gnd
topic_facet	Perkolation Perkolationstheorie Statistische Physik
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008489689&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV000000395
work_keys_str_mv	AT grimmettgeoffrey percolation

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