Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-27T13:43:28.110Z Has data issue: false hasContentIssue false
  • English
  • Français

Comparison of percolation probabilities

Published online by Cambridge University Press:  14 July 2016

Ludger Rüschendorf
Ludger Rüschendorf*
Affiliation:
University of Freiburg
*
∗ Postal address: Institut für Mathematische Stochastik der Albert-Ludwigs-Universität, D-7800 Freiburg im Breisgau, Hebelstrasse 27, W. Germany.
Get access Rights & Permissions [Opens in a new window]

Abstract

Some recent results of Oxley and Welsh (1979) and McDiarmid (1981) concerning Bernoulli percolation on clutters are generalized. Our results allow to consider quantitative aspects of percolation on graphs and clutters.

Keywords

PERCOLATION PROBABILITYCLUTTERRANDOM GRAPHASSOCIATION
Type
Short Communications
Information
Journal of Applied Probability , Volume 19 , Issue 4 , December 1982 , pp. 864 - 868
Copyright
Copyright © Applied Probability Trust 1982 

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

[1] Esary, J. D., Proschan, F. and Walkup, D. W. (1967) Association of random variables with applications. Ann. Math. Statist. 38, 1466–1474.Google Scholar
[2] 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 Le Cam, L. M., Springer-Verlag, New York, 61–110.Google Scholar
[3] Lehmann, E. L. (1966) Some concepts of dependence. Ann. Math. Statist. 37, 1137–1153.Google Scholar
[4] Mcdiarmid, C. (1981) General percolation and random graphs. Adv. Appl. Prob. 13, 40–60.CrossRefGoogle Scholar
[5] Oxley, J. G. and Welsh, D. J. A. (1979) On some percolation results of J. M. Hammersley. J. Appl. Prob. 16, 526–540.Google Scholar
[6] Rüschendorf, L. (1980) Inequalities for the expectation of ?-monotone functions. Z. Wahrscheinlichkeitsth. 54, 341–349.Google Scholar
[7] Smythe, R. T. and Wierman, J. C. (1978) First-Passage Percolation on the Square Lattice. Springer-Verlag, New York.Google Scholar