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Scaling limit of the recurrent biased random walk on a Galton–Watson tree

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Abstract

We show that the trace of the null recurrent biased random walk on a Galton–Watson tree properly renormalized converges to the Brownian forest. Our result extends to the setting of the random walk in random environment on a Galton–Watson tree.

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Authors and Affiliations

  1. Laboratoire de Probabilités et Modèles Aléatoires, Sorbonne Universités, UPMC Univ Paris 6, UMR 7599, 4 place Jussieu, 75005, Paris, France

    Elie Aïdékon & Loïc de Raphélis

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  1. Elie Aïdékon
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  2. Loïc de Raphélis
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Correspondence to Loïc de Raphélis.

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Aïdékon, E., de Raphélis, L. Scaling limit of the recurrent biased random walk on a Galton–Watson tree. Probab. Theory Relat. Fields 169, 643–666 (2017). https://doi.org/10.1007/s00440-016-0739-8

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  • DOI: https://doi.org/10.1007/s00440-016-0739-8

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