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Biased random walks on Galton–Watson trees
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  • Published: October 1996

Biased random walks on Galton–Watson trees

  • Russell Lyons1,
  • Robin Pemantle2 &
  • Yuval Peres3 

Probability Theory and Related Fields volume 106, pages 249–264 (1996)Cite this article

Summary.

We consider random walks with a bias toward the root on the family tree T of a supercritical Galton–Watson branching process and show that the speed is positive whenever the walk is transient. The corresponding harmonic measures are carried by subsets of the boundary of dimension smaller than that of the whole boundary. When the bias is directed away from the root and the extinction probability is positive, the speed may be zero even though the walk is transient; the critical bias for positive speed is determined.

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Authors and Affiliations

  1. Department of Mathematics, Indiana University, Bloomington, IN 47405-5701, USA (e-mail: rdlyons@ iu-math.math.indiana.edu) , , , , , , IN

    Russell Lyons

  2. Department of Mathematics, University of Wisconsin, Madison, WI 53706, USA , , , , , , US

    Robin Pemantle

  3. Department of Statistics, University of California, Berkeley, CA 94720-3860, USA , , , , , , US

    Yuval Peres

Authors
  1. Russell Lyons
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  2. Robin Pemantle
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  3. Yuval Peres
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Received: 7 July 1995 / In revised form: 9 January 1996

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Lyons, R., Pemantle, R. & Peres, Y. Biased random walks on Galton–Watson trees. Probab Theory Relat Fields 106, 249–264 (1996). https://doi.org/10.1007/s004400050064

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  • Issue Date: October 1996

  • DOI: https://doi.org/10.1007/s004400050064

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  • Mathematics Subject classification (1991): 60J80
  • 60J15
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