# Randomly biased walks on subcritical trees

```@article{BenArous2011RandomlyBW,
title={Randomly biased walks on subcritical trees},
author={G{\'e}rard Ben Arous and Alan Hammond},
journal={Communications on Pure and Applied Mathematics},
year={2011},
volume={65}
}```
• Published 20 January 2011
• Mathematics
• Communications on Pure and Applied Mathematics
As a model of trapping by biased motion in random structure, we study the time taken for a biased random walk to return to the root of a subcritical Galton‐Watson tree. We do so for trees in which these biases are randomly chosen, independently for distinct edges, according to a law that satisfies a logarithmic nonlattice condition. The mean return time of the walk is in essence given by the total conductance of the tree. We determine the asymptotic decay of this total conductance, finding it…
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