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arXiv · 1801.05043

Resistance growth of branching random networks

Dayue Chen·Yueyun Hu·Shen Lin
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Abstract

Consider a rooted infinite Galton-Watson tree with mean offspring number $m>1$, and a collection of i.i.d. positive random variables $\xi_e$ indexed by all the edges in the tree. We assign the resistance $m^d \xi_e$ 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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Dayue Chen, Yueyun Hu, Shen Lin. 2018-01-15. Resistance growth of branching random networks. https://arxiv.org/abs/1801.05043

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