Skip to main content

Advertisement

SpringerLink
Log in
Menu
Find a journal Publish with us
Search
Cart
  1. Home
  2. Probability Theory and Related Fields
  3. Article
Fast graphs for the random walker
Download PDF
Download PDF
  • Published: September 2002

Fast graphs for the random walker

  • Bálint Virág1 

Probability Theory and Related Fields volume 124, pages 50–72 (2002)Cite this article

  • 71 Accesses

  • 2 Citations

  • Metrics details

Abstract

 Consider the time T oz when the random walk on a weighted graph started at the vertex o first hits the vertex set z. We present lower bounds for T oz in terms of the volume of z and the graph distance between o and z. The bounds are for expected value and large deviations, and are asymptotically sharp. We deduce rate of escape results for random walks on infinite graphs of exponential or polynomial growth, and resolve a conjecture of Benjamini and Peres.

Download to read the full article text

Working on a manuscript?

Avoid the common mistakes

Author information

Authors and Affiliations

  1. Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA. e-mail: balint@math.mit.edu; http://www-math.mit.edu/~balint, , , , , , US

    Bálint Virág

Authors
  1. Bálint Virág
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Received: 31 October 2000 / Revised version: 5 January 2002 / Published online: 22 August 2002

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Virág, B. Fast graphs for the random walker. Probab Theory Relat Fields 124, 50–72 (2002). https://doi.org/10.1007/s004400200200

Download citation

  • Issue Date: September 2002

  • DOI: https://doi.org/10.1007/s004400200200

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Keywords

  • Lower Bound
  • Peris
  • Random Walk
  • Weighted Graph
  • Polynomial Growth
Download PDF

Working on a manuscript?

Avoid the common mistakes

Advertisement

Search

Navigation

  • Find a journal
  • Publish with us

Discover content

  • Journals A-Z
  • Books A-Z

Publish with us

  • Publish your research
  • Open access publishing

Products and services

  • Our products
  • Librarians
  • Societies
  • Partners and advertisers

Our imprints

  • Springer
  • Nature Portfolio
  • BMC
  • Palgrave Macmillan
  • Apress
  • Your US state privacy rights
  • Accessibility statement
  • Terms and conditions
  • Privacy policy
  • Help and support

167.114.118.210

Not affiliated

Springer Nature

© 2023 Springer Nature