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＜電子ブック＞
Percolation / by Geoffrey R. Grimmett
(Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics. ISSN:21969701 ; 321)

版	2nd ed. 1999.
出版者	Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
出版年	1999
本文言語	英語
大きさ	XIII, 447 p : online resource
冊子体	Percolation / Geoffrey Grimmett.
著者標目	*Grimmett, Geoffrey R author SpringerLink (Online service)
件　名	LCSH:Probabilities LCSH:Mathematical physics LCSH:Discrete mathematics FREE:Probability Theory FREE:Theoretical, Mathematical and Computational Physics FREE:Discrete Mathematics
一般注記	1 What is Percolation? -- 2 Some Basic Techniques -- 3 Critical Probabilities -- 4 The Number of Open Clusters per Vertex -- 5 Exponential Decay -- 6 The Subcritical Phase -- 7 Dynamic and Static Renormalization -- 8 The Supercritical Phase -- 9 Near the Critical Point: Scaling Theory -- 10 Near the Critical Point: Rigorous Results -- 11 Bond Percolation in Two Dimensions -- 12 Extensions of Percolation -- 13 Percolative Systems -- Appendix I. The Infinite-Volume Limit for Percolation -- Appendix II. The Subadditive Inequality -- List of Notation -- References -- Index of Names Percolation theory is the study of an idealized random medium in two or more dimensions. It is a cornerstone of the theory of spatial stochastic processes with applications in such fields as statistical physics, epidemiology, and the spread of populations. Percolation plays a pivotal role in studying more complex systems exhibiting phase transition. The mathematical theory is mature, but continues to give rise to problems of special beauty and difficulty. The emphasis of this book is upon core mathematical material and the presentation of the shortest and most accessible proofs. The book is intended for graduate students and researchers in probability and mathematical physics. Almost no specialist knowledge is assumed beyond undergraduate analysis and probability. This new volume differs substantially from the first edition through the inclusion of much new material, including: the rigorous theory of dynamic and static renormalization; a sketch of the lace expansion and mean field theory; the uniqueness of the infinite cluster; strict inequalities between critical probabilities; several essays on related fields and applications; numerous other results of significant. There is a summary of the hypotheses of conformal invariance. A principal feature of the process is the phase transition. The subcritical and supercritical phases are studied in detail. There is a guide for mathematicians to the physical theory of scaling and critical exponents, together with selected material describing the current state of the rigorous theory. To derive a rigorous theory of the phase transition remains an outstanding and beautiful problem of mathematics Accessibility summary: This PDF is not accessible. It is based on scanned pages and does not support features such as screen reader compatibility or described non-text content (images, graphs etc). However, it likely supports searchable and selectable text based on OCR (Optical Character Recognition). Users with accessibility needs may not be able to use this content effectively. Please contact us at accessibilitysupport@springernature.com if you require assistance or an alternative format Inaccessible, or known limited accessibility No reading system accessibility options actively disabled Publisher contact for further accessibility information: accessibilitysupport@springernature.com HTTP:URL=https://doi.org/10.1007/978-3-662-03981-6

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