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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: falawadi@kuc01.kuniv.edu.kw
Mokhtar Konsowa
Affiliation:
Department of Statistics and OR, Kuwait University, Safat, Kuwait, 13060 E-mail: konsowa@kuc01.kuniv.edu.kw
Zainab Najeh
Affiliation:
Department of Statistics and OR, Kuwait University, Safat, Kuwait, 13060 E-mail: zainab-najeh@hotmail.com
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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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