Resistance growth of branching random networks

2018/01/15 by Chen, Dayue, Hu, Yueyun, Lin, Shen
#60F05 #60J80 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1801.05043

Abstract

Consider a rooted infinite Galton-Watson tree with mean offspring number m>1, and a collection of i.i.d. positive random variables ξ_e indexed by all the edges in the tree. We assign the resistance m^d ξ_e to each edge e at distance d from the root. In this random electric network, we study the asymptotic behavior of the effective resistance and conductance between the root and the vertices at depth n. Our results generalize an existing work of Addario-Berry, Broutin and Lugosi on the binary tree to random branching networks.

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