Hostname: page-component-8448b6f56d-t5pn6 Total loading time: 0 Render date: 2024-04-23T06:51:16.995Z Has data issue: false hasContentIssue false
  • English
  • Français

Lower and Upper Bounds for the Time Constant of First-Passage Percolation

Published online by Cambridge University Press:  09 October 2002

SVEN ERICK ALM  and
ROBERT PARVIAINEN
SVEN ERICK ALM
Affiliation:
Department of Mathematics, Uppsala University, PO Box 480, S-751 06 Uppsala, Sweden (e-mail: sea@math.uu.se)
ROBERT PARVIAINEN
Affiliation:
Department of Mathematics, Uppsala University, PO Box 480, S-751 06 Uppsala, Sweden (e-mail: robert@math.uu.se)
Get access Rights & Permissions [Opens in a new window]

Abstract

We present improved lower and upper bounds for the time constant of first-passage percolation on the square lattice. For the case of lower bounds, a new method, using the idea of a transition matrix, has been used. Numerical results for the exponential and uniform distributions are presented. A simulation study is included, which results in new estimates and improved upper confidence limits for the time constants.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 11 , Issue 5 , September 2002 , pp. 433 - 445
Copyright
2002 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)