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＜電子ブック＞
An Introduction to Random Interlacements / by Alexander Drewitz, Balázs Ráth, Artëm Sapozhnikov
(SpringerBriefs in Mathematics. ISSN:21918201)

版	1st ed. 2014.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2014
本文言語	英語
大きさ	X, 120 p. 8 illus : online resource
著者標目	*Drewitz, Alexander author Ráth, Balázs author Sapozhnikov, Artëm author SpringerLink (Online service)
件　名	LCSH:Probabilities LCSH:Operations research LCSH:Management science LCSH:Mathematics FREE:Probability Theory FREE:Operations Research, Management Science FREE:Applications of Mathematics
一般注記	Random Walk, Green Function, Equilibrium Measure -- Random Interlacements: First Definition and Basic Properties.- Random Walk on the Torus and Random Interlacements.- Poisson Point Processes.- Random Interlacements Point Process.- Percolation of the Vacant Set.- Source of Correlations and Decorrelation via Coupling.- Decoupling Inequalities -- Phase Transition of Vu -- Coupling of Point Measures of Excursions This book gives a self-contained introduction to the theory of random interlacements. The intended reader of the book is a graduate student with a background in probability theory who wants to learn about the fundamental results and methods of this rapidly emerging field of research. The model was introduced by Sznitman in 2007 in order to describe the local picture left by the trace of a random walk on a large discrete torus when it runs up to times proportional to the volume of the torus. Random interlacements is a new percolation model on the d-dimensional lattice. The main results covered by the book include the full proof of the local convergence of random walk trace on the torus to random interlacements and the full proof of the percolation phase transition of the vacant set of random interlacements in all dimensions. The reader will become familiar with the techniques relevant to working with the underlying Poisson Process and the method of multi-scale renormalization, which helps in overcoming the challenges posed by the long-range correlations present in the model. The aim is to engage the reader in the world of random interlacements by means of detailed explanations, exercises and heuristics. Each chapter ends with short survey of related results with up-to date pointers to the literature HTTP:URL=https://doi.org/10.1007/978-3-319-05852-8

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