Random Walks on Trees and an Inequality of Means

Christiane Takacs and Roland Takacs ()
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Roland Takacs: Universität Linz

Journal of Theoretical Probability, 1998, vol. 11, issue 3, 701-714

Abstract: 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.

Keywords: Trees; random walks; speed; inequality; mean; harmonic; geometric; arithmetic; Jensen's Inequality (search for similar items in EconPapers)
Date: 1998
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Citations: View citations in EconPapers (1)

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DOI: 10.1023/A:1022602614733

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