Happy Holidays! Over 120,000 eBooks at just 19.99 each— Pick a favorite today

CRM Short Courses

Progress in High-Dimensional Percolation and Random Graphs

Authors: Heydenreich, Markus, van der Hofstad, Remco

  • Contains over 90 exercises designed to enhance the reader’s understanding of the material
  • Presents an introduction to percolation, as well as sources for textbooks that mainly focus on percolation
  • Gives a self-contained proof of mean-field behavior for high-dimensional percolation
  • Discusses recent extensions and additions to classical results
see more benefits

Buy this book

eBook $54.99
price for USA (gross)
  • ISBN 978-3-319-62473-0
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $69.99
price for USA
  • ISBN 978-3-319-62472-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

This text presents an engaging exposition of the active field of high-dimensional percolation that will likely provide an impetus for future work. With over 90 exercises designed to enhance the reader’s understanding of the material, as well as many open problems, the book is aimed at graduate students and researchers who wish to enter the world of this rich topic.  The text may also be useful in advanced courses and seminars, as well as for reference and individual study.

Part I, consisting of 3 chapters, presents a general introduction to percolation, stating the main results, defining the central objects, and proving its main properties. No prior knowledge of percolation is assumed. Part II, consisting of Chapters 4–9, discusses mean-field critical behavior by describing the two main techniques used, namely, differential inequalities and the lace expansion. In Parts I and II, all results are proved, making this the first self-contained text discussing high-dime

nsional percolation.  Part III, consisting of Chapters 10–13, describes recent progress in high-dimensional percolation.   Partial proofs and substantial overviews of how the proofs are obtained are given. In many of these results, the lace expansion and differential inequalities or their discrete analogues are central. Part IV, consisting of Chapters 14–16, features related models and further open problems, with a focus on the big picture.

About the authors

Markus Heydenreich is a professor of Applied Mathematics at Ludwig-Maximilians-Universität München. Professor Heydenreich works in Probability theory, he investigates random spatial structures.

Remco van der Hofstad is a professor in Mathematics at Eindhoven University of Technology and scientific director of Eurandom. He received the Prix Henri Poincaré 2003 jointly with Gordon Slade and the Rollo Davidson Prize in 2007. He works on high-dimensional statistical physics,  random graphs as models for complex networks, and applications of probability to related fields such as electrical engineering, computer science and chemistry.

Video

Table of contents (16 chapters)

  • Introduction and Motivation

    Heydenreich, Markus (et al.)

    Pages 3-18

  • Fixing Ideas: Percolation on a Tree and Branching Random Walk

    Heydenreich, Markus (et al.)

    Pages 19-29

  • Uniqueness of the Phase Transition

    Heydenreich, Markus (et al.)

    Pages 31-44

  • Critical Exponents and the Triangle Condition

    Heydenreich, Markus (et al.)

    Pages 47-54

  • Proof of Triangle Condition: The Infrared Bound

    Heydenreich, Markus (et al.)

    Pages 55-64

Buy this book

eBook $54.99
price for USA (gross)
  • ISBN 978-3-319-62473-0
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $69.99
price for USA
  • ISBN 978-3-319-62472-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Loading...

Recommended for you

Loading...

Bibliographic Information

Bibliographic Information
Book Title
Progress in High-Dimensional Percolation and Random Graphs
Authors
Series Title
CRM Short Courses
Copyright
2017
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-62473-0
DOI
10.1007/978-3-319-62473-0
Hardcover ISBN
978-3-319-62472-3
Series ISSN
2522-5200
Edition Number
1
Number of Pages
XII, 285
Number of Illustrations and Tables
9 b/w illustrations, 1 illustrations in colour
Topics