École d'Été de Probabilités de Saint-Flour

Random Walks on Disordered Media and their Scaling Limits

École d'Été de Probabilités de Saint-Flour XL - 2010

Authors: Kumagai, Takashi

  • Starts from basics on discrete potential theory
  • Contains many interesting examples of disordered media with anomalous heat conduction
  • Anomalous behavior of random walk at criticality on random media
  • Contains recent developments on random conductance models
see more benefits

Buy this book

eBook $39.99
price for USA (gross)
  • ISBN 978-3-319-03152-1
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $49.99
price for USA
  • ISBN 978-3-319-03151-4
  • 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

In these lecture notes, we will analyze the behavior of random walk on disordered media by means of both probabilistic and analytic methods, and will study the scaling limits. We will focus on the discrete potential theory and how the theory is effectively used in the analysis of disordered media. The first few chapters of the notes can be used as an introduction to discrete potential theory.
Recently, there has been significant progress on the theory of random walk on disordered media such as fractals and random media. Random walk on a percolation cluster(‘the ant in the labyrinth’)is one of the typical examples. In 1986, H. Kesten showed the anomalous behavior of a random walk on a percolation cluster at critical probability. Partly motivated by this work, analysis and diffusion processes on fractals have been developed since the late eighties. As a result, various new methods have been produced to estimate heat kernels on disordered media. These developments are summarized in the notes.

Table of contents (8 chapters)

  • Introduction

    Kumagai, Takashi

    Pages 1-2

  • Weighted Graphs and the Associated Markov Chains

    Kumagai, Takashi

    Pages 3-19

  • Heat Kernel Estimates: General Theory

    Kumagai, Takashi

    Pages 21-41

  • Heat Kernel Estimates Using Effective Resistance

    Kumagai, Takashi

    Pages 43-58

  • Heat Kernel Estimates for Random Weighted Graphs

    Kumagai, Takashi

    Pages 59-64

Buy this book

eBook $39.99
price for USA (gross)
  • ISBN 978-3-319-03152-1
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $49.99
price for USA
  • ISBN 978-3-319-03151-4
  • 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
Random Walks on Disordered Media and their Scaling Limits
Book Subtitle
École d'Été de Probabilités de Saint-Flour XL - 2010
Authors
Series Title
École d'Été de Probabilités de Saint-Flour
Series Volume
2101
Copyright
2014
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-03152-1
DOI
10.1007/978-3-319-03152-1
Softcover ISBN
978-3-319-03151-4
Series ISSN
0721-5363
Edition Number
1
Number of Pages
X, 147
Number of Illustrations and Tables
5 b/w illustrations
Topics