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Bounds on the speed and on regeneration times for certain processes on regular trees

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Author Info

  • Andrea Collevecchio

    ()
    (Dept. of Applied Mathematics and Advanced School of Economics)

  • Tom Schmitz

    ()
    (Max Planck Institute for Mathematics in the Sciences)

Abstract

We develop a technique that provides a lower bound on the speed of transient random walk in a random environment on regular trees. A refinement of this technique yields upper bounds on the first regeneration level and regeneration time. In particular, a lower and upper bound on the covariance in the annealed invariance principle follows. We emphasize the fact that our methods are general and also apply in the case of once-reinforced random walk. Durrett, Kesten and Limic [11] prove an upper bound of the form b/(b + d) for the speed on the b-ary tree, where d is the reinforcement parameter. For d > 1 we provide a lower bound of the form g^2b/(b + d), where g is the survival probability of an associated branching process.

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File URL: http://virgo.unive.it/wpideas/storage/2009wp192.pdf
File Function: First version, 2009
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Bibliographic Info

Paper provided by Department of Applied Mathematics, Università Ca' Foscari Venezia in its series Working Papers with number 192.

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Length: 22 pages
Date of creation: Nov 2009
Date of revision:
Handle: RePEc:vnm:wpaper:192

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Related research

Keywords: Random walk in a random environment; once edge-reinforced random walk; lower bound on the speed; regeneration times; regular trees.;

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