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140122 ||| eng |
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|a 9781475742084
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|a Grimmett, Geoffrey
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|a Percolation
|h Elektronische Ressource
|c by Geoffrey Grimmett
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|a 1st ed. 1989
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|a New York, NY
|b Springer New York
|c 1989, 1989
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| 300 |
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|a XI, 296 p. 1 illus
|b online resource
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|a 1 What Is Percolation? -- 2 Some Basic Techniques -- 3 The Uniqueness of the Critical Point -- 4 The Number of Open Clusters per Vertex -- 5 The Subcritical Phase -- 6 The Supercritical Phase -- 7 Near the Critical Point: Scaling Theory -- 8 Near the Critical Point: Rigorous Results -- 9 Bond Percolation in Two Dimensions -- 10 A Miscellany of Random Processes -- Appendix I. The Infinite-Volume Limit for Percolation -- Appendix II. The Subadditive Inequality -- List of Notation -- References -- Index of Names
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| 653 |
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|a Quantum Physics
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| 653 |
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|a Complex Systems
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| 653 |
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|a Probability Theory
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| 653 |
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|a System theory
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| 653 |
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|a Quantum physics
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| 653 |
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|a Mathematical physics
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| 653 |
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|a Theoretical, Mathematical and Computational Physics
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| 653 |
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|a Probabilities
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|a eng
|2 ISO 639-2
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| 989 |
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|b SBA
|a Springer Book Archives -2004
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|a 10.1007/978-1-4757-4208-4
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|u https://doi.org/10.1007/978-1-4757-4208-4?nosfx=y
|x Verlag
|3 Volltext
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|a 530.1
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|a Quite apart from the fact that percolation theory had its ongm in an honest applied problem, it is a source of fascinating problems of the best kind for which a mathematician can wish: problems which are easy to state with a minimum of preparation, but whose solutions are apparently difficult and require new methods. At the same time, many of the prob lems are of interest to or proposed by statistical physicists and not dreamed up merely to demonstrate ingenuity. Much progress has been made in recent years, and many of the open problems of ten years aga have been solved. With such solutions we have seen the evolution of new techniques and questions; the consequent knowledge has shifted the ground under percolation, and it is time to examine afresh the mathematics of the subject. The quantity of literature related to percolation seems to grow hour by hour, mostly in the physics journals. It is becoming increasingly diffi cult to get to know the subject from scratch, and one of the principal purposes of this book is to remedy this. This book is about the mathematics of percolation theory, with the emphasis upon presenting the shortest rigorous proofs of the main facts
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