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Random Walks on Trees and an Inequality of Means

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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.

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Authors and Affiliations

  1. Institut für Mathematik, Universität Linz, Altenbergerstasse 69, 4040, Linz

    Roland Takacs

Authors
  1. Christiane Takacs
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  2. Roland Takacs
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Takacs, C., Takacs, R. Random Walks on Trees and an Inequality of Means. Journal of Theoretical Probability 11, 701–714 (1998). https://doi.org/10.1023/A:1022602614733

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  • DOI: https://doi.org/10.1023/A:1022602614733

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