# Resistance growth of branching random networks

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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Cited literature [12 references]

https://hal.archives-ouvertes.fr/hal-01688502
Contributor : Shen Lin <>
Submitted on : Friday, May 18, 2018 - 2:36:02 PM
Last modification on : Tuesday, May 5, 2020 - 1:03:21 PM
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• HAL Id : hal-01688502, version 2

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Dayue Chen, Yueyun Hu, Shen Lin. Resistance growth of branching random networks. 2018. ⟨hal-01688502v2⟩

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