Dimensions of random trees

Mokhtar H. Konsowa and Tamer F. Oraby

Statistics & Probability Letters, 2003, vol. 62, issue 1, pages 49-60

Abstract: In this paper we show, for Galton-Watson tree T of resistance R, that R-Rn decays exponentially in n where Rn 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.

Keywords: Random; trees; Galton-Waston; tree; Random; walks (search for similar items in EconPapers)
Date: 2003
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