Conductance of a subdiffusive random weighted tree

Pierre Rousselin

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arXiv · 1905.00821

Conductance of a subdiffusive random weighted tree

Pierre Rousselin

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Abstract

We work on a Galton--Watson tree with random weights, in the so-called "subdiffusive" regime. We study the rate of decay of the conductance between the root and the $n$-th level of the tree, as $n$ goes to infinity, by a mostly analytic method. It turns out the order of magnitude of the expectation of this conductance can be less than $1/n$ (in contrast with the results of Addario-Berry-Broutin-Lugosi and Chen-Hu-Lin), depending on the value of the second zero of the characteristic function associated to the model. We also prove the almost sure (and in $L^p$ for some $p>1$) convergence of this conductance divided by its expectation towards the limit of the additive martingale.

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Pierre Rousselin. 2019-05-02. Conductance of a subdiffusive random weighted tree. https://arxiv.org/abs/1905.00821

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