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CONDUCTIVITY OF RANDOM TREES

Published online by Cambridge University Press:  21 May 2002

Mokhtar H. Konsowa
Mokhtar H. Konsowa
Affiliation:
Department of Mathematics, Faculty of Science, Helwan University, Helwan, Cairo, Egypt, E-mail: [email protected]
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Abstract

We prove that the effective resistances of spherically symmetric random trees dominate in mean the effective resistances of random trees corresponding branching processes in varying environments and having the same growth law of spherically symmetric trees. We conjecture that the statement does not necessarily hold true in the case of stochastic domination and give an idea of constructing a counterexample.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 16 , Issue 2 , April 2002 , pp. 233 - 240
Copyright
© 2002 Cambridge University Press

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