On the Local Time of the Half-Plane Half-Comb Walk

Endre Csáki () and Antónia Földes ()
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Endre Csáki: Alfréd Rényi Institute of Mathematics
Antónia Földes: CUNY

Journal of Theoretical Probability, 2022, vol. 35, issue 2, 1247-1261

Abstract: Abstract The Half-Plane Half-Comb walk is a random walk on the plane, when we have a square lattice on the upper half-plane and a comb structure on the lower half-plane, i.e., horizontal lines below the x-axis are removed. We prove that the probability that this walk returns to the origin in 2N steps is asymptotically equal to $$2/(\pi N).$$ 2 / ( π N ) . As a consequence, we prove strong laws and a limit distribution for the local time.

Keywords: Anisotropic random walk; Strong approximation; Wiener process; Local time; Laws of the iterated logarithm; Primary 60F05; 60G50; Secondary 60F15 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10959-020-01065-2

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