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Localization Transition of Biased Random Walks on Random Networks

Vishal Sood·Peter Grassberger
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Abstract

We study random walks on large random graphs that are biased towards a randomly chosen but fixed target node. We show that a critical bias strength b_c exists such that most walks find the target within a finite time when b>b_c. For b<b_c, a finite fraction of walks drifts off to infinity before hitting the target. The phase transition at b=b_c is second order, but finite size behavior is complex and does not obey the usual finite size scaling ansatz. By extending rigorous results for biased walks on Galton-Watson trees, we give the exact analytical value for b_c and verify it by large scale simulations.

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BibTeXRIS

Vishal Sood, Peter Grassberger. 2007-08-27. Localization Transition of Biased Random Walks on Random Networks. https://doi.org/10.1103/physrevlett.99.098701

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