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


  • Andrea Collevecchio

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

  • Tom Schmitz

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


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.

Suggested Citation

  • Andrea Collevecchio & Tom Schmitz, 2009. "Bounds on the speed and on regeneration times for certain processes on regular trees," Working Papers 192, Department of Applied Mathematics, Universit√† Ca' Foscari Venezia.
  • Handle: RePEc:vnm:wpaper:192

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

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C00 - Mathematical and Quantitative Methods - - General - - - General

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