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June 2011 Bounds on the speed and on regeneration times for certain processes on regular trees
Andrea Collevecchio, Tom Schmitz
Ann. Appl. Probab. 21(3): 1073-1101 (June 2011). DOI: 10.1214/10-AAP719

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 [Probab. Theory Related Fields. 122 (2002) 567–592] prove an upper bound of the form b/(b+δ) for the speed on the b-ary tree, where δ is the reinforcement parameter. For δ>1 we provide a lower bound of the form γ2b/(b+δ), where γ is the survival probability of an associated branching process.

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Andrea Collevecchio. Tom Schmitz. "Bounds on the speed and on regeneration times for certain processes on regular trees." Ann. Appl. Probab. 21 (3) 1073 - 1101, June 2011. https://doi.org/10.1214/10-AAP719

Information

Published: June 2011
First available in Project Euclid: 2 June 2011

zbMATH: 1225.60156
MathSciNet: MR2830613
Digital Object Identifier: 10.1214/10-AAP719

Subjects:
Primary: 60K37 , 60K99

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

Rights: Copyright © 2011 Institute of Mathematical Statistics

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Vol.21 • No. 3 • June 2011
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