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Bosi, Gianluca; Hu, Yiping; Peres, Yuval

Recurrence and windings of two revolving random walks. (English) Zbl 1503.60054

Electron. J. Probab. 27, Paper No. 66, 22 p. (2022).
In this paper, the authors study asymptotic properties and windings behaviors of two oriented random walks, (thus) non-reversible and non-elliptic, which are both bound to revolve clockwise on the plane but show different asymptotic behaviors. They only differ by the possible transitions on the horizontal axis but this is enough to get a distinction recurrence vs. transience, which in turns manifests itself into different windings behaviors. The proofs are based on the derivation of limit theorems for specific random times of auxiliary random walks, using among others standard probability results as the Chung-Feller theorem, conditional Markov estimates, rates of decays for return probabilities, Lyapunov functions, etc. The authors also obtain scaling limits of the random walks and of corresponding windings.
Reviewer: Arnaud Le Ny (Paris)

Cited in 1 Document

MSC:

60G50 Sums of independent random variables; random walks
60J10 Markov chains (discrete-time Markov processes on discrete state spaces)

Keywords:

oriented lattices; transience/recurrence; Lyapounov functions; winding
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References:

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