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2018 On the speed of once-reinforced biased random walk on trees
Andrea Collevecchio, Mark Holmes, Daniel Kious
Electron. J. Probab. 23: 1-32 (2018). DOI: 10.1214/18-EJP208

Abstract

We study the asymptotic behaviour of once-reinforced biased random walk (ORbRW) on Galton-Watson trees. Here the underlying (unreinforced) random walk has a bias towards or away from the root. We prove that in the setting of multiplicative once-reinforcement the ORbRW can be recurrent even when the underlying biased random walk is ballistic. We also prove that, on Galton-Watson trees without leaves, the speed is positive in the transient regime. Finally, we prove that, on regular trees, the speed of the ORbRW is monotone decreasing in the reinforcement parameter when the underlying random walk has high speed, and the reinforcement parameter is small.

Citation

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Andrea Collevecchio. Mark Holmes. Daniel Kious. "On the speed of once-reinforced biased random walk on trees." Electron. J. Probab. 23 1 - 32, 2018. https://doi.org/10.1214/18-EJP208

Information

Received: 6 September 2017; Accepted: 27 July 2018; Published: 2018
First available in Project Euclid: 12 September 2018

zbMATH: 06964780
MathSciNet: MR3858914
Digital Object Identifier: 10.1214/18-EJP208

Subjects:
Primary: 60K35

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