Electronic Journal of Probability

Resistance growth of branching random networks

Dayue Chen, Yueyun Hu, and Shen Lin

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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.

Article information

Electron. J. Probab., Volume 23 (2018), paper no. 52, 17 pp.

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

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Zentralblatt MATH identifier

Primary: 60F05: Central limit and other weak theorems 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)

electric networks Galton–Watson tree random conductance

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Chen, Dayue; Hu, Yueyun; Lin, Shen. Resistance growth of branching random networks. Electron. J. Probab. 23 (2018), paper no. 52, 17 pp. doi:10.1214/18-EJP179. https://projecteuclid.org/euclid.ejp/1527818430

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