Open Access
2018 Resistance growth of branching random networks
Dayue Chen, Yueyun Hu, Shen Lin
Electron. J. Probab. 23: 1-17 (2018). DOI: 10.1214/18-EJP179


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. "Resistance growth of branching random networks." Electron. J. Probab. 23 1 - 17, 2018.


Received: 16 January 2018; Accepted: 17 May 2018; Published: 2018
First available in Project Euclid: 1 June 2018

zbMATH: 06924664
MathSciNet: MR3814246
Digital Object Identifier: 10.1214/18-EJP179

Primary: 60F05 , 60J80

Keywords: electric networks , Galton–Watson tree , random conductance

Vol.23 • 2018
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