Commute times and the effective resistances of random trees

Authors:
Fahimah Al-awadhi;Mokhtar Konsowa;Zainab Najeh
Affiliations:
Department of statistics and or, kuwait university, safat, kuwait, 13060 e-mail: falawadi@kuc01.kuniv.edu.kw;Department of statistics and or, kuwait university, safat, kuwait, 13060 e-mail: konsowa@kuc01.kuniv.edu.kw;Department of statistics and or, kuwait university, safat, kuwait, 13060 e-mail: zainab-najeh@hotmail.com
Venue:
Probability in the Engineering and Informational Sciences
Year:
2009

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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.