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THE SPEED OF RANDOM WALKS ON TREES AND ELECTRIC NETWORKS

Published online by Cambridge University Press:  17 November 2011

Mokhtar Konsowa  and
Fahimah Al-Awadhi
Mokhtar Konsowa
Affiliation:
Department of Statistics and Operations Research, Faculty of Science, Kuwait University, Safat 13060, Kuwait E-mail: [email protected]; [email protected]
Fahimah Al-Awadhi
Affiliation:
Department of Statistics and Operations Research, Faculty of Science, Kuwait University, Safat 13060, Kuwait E-mail: [email protected]; [email protected]
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Abstract

The speed of the random walk on a tree is the rate of escaping its starting point. It depends on the way that the branching occurs in the sense that if the average number of branching is large, the speed is more likely to be positive. The speed on some models of random trees is calculated via calculating the hitting times of the consecutive levels of the tree.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 26 , Issue 1 , January 2012 , pp. 105 - 116
Copyright
Copyright © Cambridge University Press 2011

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References

REFERENCES

1.Al-Awadhi, F., Konsowa, M. & Najeh, Z. (2009). Commute times and the effective resistances of random trees. Probability in the Engineering and Informational Sciences, 23(4): 649–660.CrossRefGoogle Scholar
2.Aldous, D. & Fill, J. (1999). Reversible Markov chains and random walks on graphs. Preprint. Available from http://www.stat.berkeley.edu/~aldous/book.html.Google Scholar
3.Doyle, P. & Snell, L. (1984). Random walks and electric networks. The Carus Mathematical Monographs. Washington, DC: Mathematical Association of America.CrossRefGoogle Scholar
4.Konsowa, M. (2009). On the speed of random walks on random trees. Statistics and Probability Letters 79: 2230–2236.CrossRefGoogle Scholar
5.Konsowa, M. & Mitro, J. (1991). The type problem of random walks on trees. Journal of Theoretic Probabilities 4(3): 535–550.CrossRefGoogle Scholar
6.Lyons, R. (1990). Random walks and percolation on trees. Annals of Probability 18: 931–958.CrossRefGoogle Scholar
7.Lyons, R. (1992). Random walks, capacity, and percolation on trees. Annals of Probability 20: 2043–2088.Google Scholar
8.Lyons, R. & Peres, Y. (2011) Probability on trees and networks. Cambridge: Cambridge University Press.Google Scholar
9.Peres, Y. (1999). Probability on trees: An introductory climb. Ecole d'Ete de Probabilities de Saint Flour XXVII—1997, Lectures Notes in Mathematics Vol. 1717, Berlin: Springer, pp. 193–280.Google Scholar