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Random Walks on Trees and an Inequality of Means

Author

Listed:
  • Christiane Takacs
  • Roland Takacs

    (Universität Linz)

Abstract

We define trees generated by bi-infinite sequences, calculate their walk-invariant distribution and the speed of a biased random walk. We compare a simple random walk on a tree generated by a bi-infinite sequence with a simple random walk on an augmented Galton-Watson tree. We find that comparable simple random walks require the augmented Galton-Watson tree to be larger than the corresponding tree generated by a bi-infinite sequence. This is due to an inequality for random variables with values in [1, ∞[ involving harmonic, geometric and arithmetic mean.

Suggested Citation

  • Christiane Takacs & Roland Takacs, 1998. "Random Walks on Trees and an Inequality of Means," Journal of Theoretical Probability, Springer, vol. 11(3), pages 701-714, July.
    • Handle: RePEc:spr:jotpro:v:11:y:1998:i:3:d:10.1023_a:1022602614733
    DOI: 10.1023/A:1022602614733
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    Cited by:

    1. Christiane Takacs, 2001. "More Randomness of Environment Does Not Always Slow Down a Random Walk," Journal of Theoretical Probability, Springer, vol. 14(3), pages 699-715, July.

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