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Cover: 9780521872324 | Percolation | Oliver Riordan | Buch | HC gerader Rücken kaschiert
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Percolation
Buch von Oliver Riordan
Sprache: Englisch

102,95 €*

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Lieferzeit 2-3 Wochen

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Beschreibung
Percolation theory was initiated some fifty years ago as a mathematical framework for the study of random physical processes such as flow through a disordered porous medium. It has proved to be a remarkably rich theory, with applications beyond natural phenomena to topics such as network modelling. The aims of this book are twofold. First to present classical results in a way that is accessible to non-specialists. Second, to describe, for the first time in a book, recent results of Smirnov in conformal invariance, and outline the proof that the critical probability for random Voronoi percolation in the plane is 1/2. Throughout, the presentation is streamlined, with elegant and straightforward proofs requiring minimal background in probability and graph theory. Numerous examples illustrate the important concepts and enrich the arguments. All-in-all, it will be an essential purchase for mathematicians, physicists, electrical engineers and computer scientists working in this exciting area.
Percolation theory was initiated some fifty years ago as a mathematical framework for the study of random physical processes such as flow through a disordered porous medium. It has proved to be a remarkably rich theory, with applications beyond natural phenomena to topics such as network modelling. The aims of this book are twofold. First to present classical results in a way that is accessible to non-specialists. Second, to describe, for the first time in a book, recent results of Smirnov in conformal invariance, and outline the proof that the critical probability for random Voronoi percolation in the plane is 1/2. Throughout, the presentation is streamlined, with elegant and straightforward proofs requiring minimal background in probability and graph theory. Numerous examples illustrate the important concepts and enrich the arguments. All-in-all, it will be an essential purchase for mathematicians, physicists, electrical engineers and computer scientists working in this exciting area.
Über den Autor
Béla Bollobás is a Senior Research Fellow at Trinity College, Cambridge and is the Jabie Hardin Chair of Excellence in Combinatorics at the University of Memphis. He has held visiting positions from Seattle to Singapore, from Brazil to Zurich. This is his eleventh book.
Inhaltsverzeichnis
Preface; 1. Basic concepts; 2. Probabilistic tools; 3. Percolation on Z2 - the Harris-Kesten theorem; 4. Exponential decay and critical probabilities - theorems of Menshikov and Aizenman & Barsky; 5. Uniqueness of the infinite open cluster and critical probabilities; 6. Estimating critical probabilities; 7. Conformal invariance - Smirnov's theorem; 8. Continuum percolation; Bibliography; Index; List of notation.
Details
Erscheinungsjahr: 2013
Fachbereich: Analysis
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Seiten: 334
ISBN-13: 9780521872324
ISBN-10: 0521872324
Sprache: Englisch
Ausstattung / Beilage: HC gerader Rücken kaschiert
Einband: Gebunden
Autor: Riordan, Oliver
Hersteller: Cambridge University Press
Maße: 235 x 157 x 23 mm
Von/Mit: Oliver Riordan
Erscheinungsdatum: 30.04.2013
Gewicht: 0,638 kg
preigu-id: 102141273
Über den Autor
Béla Bollobás is a Senior Research Fellow at Trinity College, Cambridge and is the Jabie Hardin Chair of Excellence in Combinatorics at the University of Memphis. He has held visiting positions from Seattle to Singapore, from Brazil to Zurich. This is his eleventh book.
Inhaltsverzeichnis
Preface; 1. Basic concepts; 2. Probabilistic tools; 3. Percolation on Z2 - the Harris-Kesten theorem; 4. Exponential decay and critical probabilities - theorems of Menshikov and Aizenman & Barsky; 5. Uniqueness of the infinite open cluster and critical probabilities; 6. Estimating critical probabilities; 7. Conformal invariance - Smirnov's theorem; 8. Continuum percolation; Bibliography; Index; List of notation.
Details
Erscheinungsjahr: 2013
Fachbereich: Analysis
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Seiten: 334
ISBN-13: 9780521872324
ISBN-10: 0521872324
Sprache: Englisch
Ausstattung / Beilage: HC gerader Rücken kaschiert
Einband: Gebunden
Autor: Riordan, Oliver
Hersteller: Cambridge University Press
Maße: 235 x 157 x 23 mm
Von/Mit: Oliver Riordan
Erscheinungsdatum: 30.04.2013
Gewicht: 0,638 kg
preigu-id: 102141273
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