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COMMUTE TIMES AND THE EFFECTIVE RESISTANCES OF RANDOM TREES

Published online by Cambridge University Press:  14 July 2009

Fahimah Al-Awadhi ,
Mokhtar Konsowa  and
Zainab Najeh
Fahimah Al-Awadhi
Affiliation:
Department of Statistics and OR, Kuwait University, Safat, Kuwait, 13060 E-mail: [email protected]
Mokhtar Konsowa
Affiliation:
Department of Statistics and OR, Kuwait University, Safat, Kuwait, 13060 E-mail: [email protected]
Zainab Najeh
Affiliation:
Department of Statistics and OR, Kuwait University, Safat, Kuwait, 13060 E-mail: [email protected]
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Abstract

In this article we study the commute and hitting times of simple random walks on spherically symmetric random trees in which every vertex of level n has outdegree 1 with probability 1−qn and outdegree 2 with probability qn. Our argument relies on the link between the commute times and the effective resistances of the associated electric networks when 1 unit of resistance is assigned to each edge of the tree.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 23 , Issue 4 , October 2009 , pp. 649 - 660
Copyright
Copyright © Cambridge University Press 2009

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References

1.Aldous, D. & Fill, J. (2002). Reversible Markov chains and random walks on graphs. Preprint. Available from http://www.stat.berkeley.edu/~aldous/book.html.Google Scholar
2.Chandra, A., Reghavan, P., Ruzzo, W., Smolensky, R., & Tiwari, P. (1989). The electrical resistance of a graph captures its commute and cover times. Proceedings of the annual ACM symposium on the theory of computing, pp. 574–586.CrossRefGoogle Scholar
3.Doyle, P. & Snell, J. (1984). Random walks and electric networks. The Carus Mathematical Monographs. Washington, DC: Mathematical Association of America.CrossRefGoogle Scholar
4.Feller, W. (1968). An introduction to probability theory and its applications, Vol. I, 2nd ed.New York: Wiley.Google Scholar
5.Knopp, K. (1956). Infinite sequences and series. New York: Dover Publications.Google Scholar
6.Konsowa, M. (2006). Random walks on finite graphs. Journal of Statistical Theory and Its Applications 5(4): 373–380.Google Scholar
7.Lovász, L. (1993). Random walks on graphs. Bolyai Society, Mathematical Studies 2: 1–46.Google Scholar