An introduction to random interlacements / Alexander Drewitz, Balázs Ráth, Artëm Sapozhnikov.

An introduction to random interlacements / Alexander Drewitz, Balázs Ráth, Artëm Sapozhnikov.

9783319058528 electronic book
3319058525 electronic book
9783319058511

Cham : Springer, 2014.

English

1 online resource (x, 120 pages) : illustrations.

10.1007/978-3-319-05852-8 doi

QA273

519.2

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.

Includes bibliographical references and index.

Access limited to authorized users.

Description based on online resource; title from PDF title page (SpringerLink, viewed May 16, 2014).

SpringerBriefs in mathematics, 2191-8198

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