SpringerBriefs in Mathematics

An Introduction to Random Interlacements

Authors: Drewitz, Alexander, Ráth, Balázs, Sapozhnikov, Artem

  • Essentially self-contained introduction to random interlacements on advanced undergraduate/graduate student level
  • Based on lecture notes for a topics class at ETH Zurich held by the three authors
  • Includes chapter summaries and detailed illustrations
see more benefits

Buy this book

eBook $39.99
price for USA (gross)
  • ISBN 978-3-319-05852-8
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $54.99
price for USA
  • ISBN 978-3-319-05851-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
About this book

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.

Table of contents (10 chapters)

  • Random Walk, Green Function, and Equilibrium Measure

    Drewitz, Alexander (et al.)

    Pages 1-9

  • Random Interlacements: First Definition and Basic Properties

    Drewitz, Alexander (et al.)

    Pages 11-18

  • Random Walk on the Torus and Random Interlacements

    Drewitz, Alexander (et al.)

    Pages 19-29

  • Poisson Point Processes

    Drewitz, Alexander (et al.)

    Pages 31-35

  • Random Interlacement Point Process

    Drewitz, Alexander (et al.)

    Pages 37-50

Buy this book

eBook $39.99
price for USA (gross)
  • ISBN 978-3-319-05852-8
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $54.99
price for USA
  • ISBN 978-3-319-05851-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
Loading...

Recommended for you

Loading...

Bibliographic Information

Bibliographic Information
Book Title
An Introduction to Random Interlacements
Authors
Series Title
SpringerBriefs in Mathematics
Copyright
2014
Publisher
Springer International Publishing
Copyright Holder
The Author(s)
eBook ISBN
978-3-319-05852-8
DOI
10.1007/978-3-319-05852-8
Softcover ISBN
978-3-319-05851-1
Series ISSN
2191-8198
Edition Number
1
Number of Pages
X, 120
Number of Illustrations and Tables
8 b/w illustrations
Topics