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

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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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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Keywords

  • Random walk
  • Galton–Watson tree
  • Scaling limit

Mathematics Subject Classification

  • 60J80
  • 60G50
  • 60F17