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Pré-Publication, Document De Travail Année : 2018

Resistance growth of branching random networks

Résumé

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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Dates et versions

hal-01688502 , version 1 (19-01-2018)
hal-01688502 , version 2 (18-05-2018)

Identifiants

  • HAL Id : hal-01688502 , version 1

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Dayue Chen, Yueyun Hu, Shen Lin. Resistance growth of branching random networks. 2018. ⟨hal-01688502v1⟩
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