Hostname: page-component-848d4c4894-5nwft Total loading time: 0 Render date: 2024-06-08T12:44:34.266Z Has data issue: false hasContentIssue false
  • English
  • Français

First-passage percolation processes with finite height

Published online by Cambridge University Press:  14 July 2016

Norbert Herrndorf
Norbert Herrndorf*
Affiliation:
Universität Köln
*
∗ Postal address: Mathematisches Institut der Universität Köln, Weyerthal 86–90, D-5000 Köln 41, West Germany.
Get access Rights & Permissions [Opens in a new window]

Abstract

We consider first-passage percolation in an infinite horizontal strip of finite height. Using methods from the theory of Markov chains, we prove a central limit theorem for first-passage times, and compute the time constants for some special cases.

Keywords

TIME CONSTANTCENTRAL LIMIT THEOREM FOR FIRST-PASSAGE TIMESBERNOULLI PERCOLATION
Type
Research Papers
Information
Journal of Applied Probability , Volume 22 , Issue 4 , December 1985 , pp. 766 - 775
Copyright
Copyright © Applied Probability Trust 1985 

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.)

References

Cox, J. T. (1980) The time constant of first-passage percolation on the square lattice. Adv. Appl. Prob. 12, 864–879.Google Scholar
Dobrushin, R. L. (1956) Central limit theorem for nonstationary Markov chains. Theory Prob. Appl. 1, 65–80; 329-383.Google Scholar
Doob, J. L. (1953) Stochastic Processes. Wiley, New York.Google Scholar
Hammersley, J. M. and Welsh, D. J. A. (1965) First passage percolation, subadditive processes, stochastic networks, and generalized renewal theory. In Bernoulli-Bayes-Laplace Anniversary Volume , ed. Neyman, J. and LeCam, L. M., Springer-Verlag, Berlin.Google Scholar
Ibragimov, I. A. (1962) Some limit theorems for stationary processes. Theory Prob. Appl. 7, 349–382.Google Scholar
Iosifescu, M. and Theodorescu, R. (1969) Random Processes and Learning. Springer-Verlag, Berlin.Google Scholar
Kingman, J. F. C. (1968) The ergodic theory of subadditive stochastic processes. J. R. Statist. Soc. B 30, 499–510.Google Scholar
Smythe, R. T. and Wierman, J. C. (1978) First Passage Percolation on the Square Lattice. Lecture Notes in Mathematics 671, Springer-Verlag, Berlin.Google Scholar
Wierman, J. C. (1982) Percolation theory. Ann. Prob. 10, 509–524.Google Scholar