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Dimensions of random trees

✍ Scribed by Mokhtar H. Konsowa; Tamer F. Oraby

Publisher: Elsevier Science
Year: 2003
Tongue: English
Weight: 158 KB
Volume: 62
Category: Article
ISSN: 0167-7152
DOI: 10.1016/s0167-7152(02)00424-8

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✦ Synopsis

In this paper we show, for Galton-Watson tree T of resistance R, that R -R n decays exponentially in n where R n denotes the resistance of the portion of T between the root and level n. We also determine a formula for the resistance dimension of spherically symmetric random trees and prove that it is equal to the fractal dimension. We emphasize the relationship between these dimensions and the type, of being transient or recurrent, of the simple random walks on such trees.

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