An Introduction to Random Interlacements by Alexander DrewitzAn Introduction to Random Interlacements by Alexander Drewitz

An Introduction to Random Interlacements

byAlexander Drewitz, Art Sapozhnikov, Artëm Sapozhnikov

Paperback | May 21, 2014

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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.
Title:An Introduction to Random InterlacementsFormat:PaperbackDimensions:120 pagesPublished:May 21, 2014Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:3319058517

ISBN - 13:9783319058511

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Table of Contents

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 ofVu.- Coupling of Point Measures of Excursions.