An Introduction to Random Interlacements

種類:

電子ブック

責任表示:

by Alexander Drewitz, Balázs Ráth, Artëm Sapozhnikov

出版情報:

Cham : Springer International Publishing : Imprint: Springer, 2014

著者名:

• Drewitz, Alexander
• Ráth, Balázs
• Sapozhnikov, Artëm
• SpringerLink (Online service)

シリーズ名:

SpringerBriefs in Mathematics ;

ISBN:

9783319058528 [3319058525]    

注記:

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 cha

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