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On the Local Time of the Half-Plane Half-Comb Walk.
- Source :
- Journal of Theoretical Probability; Jun2022, Vol. 35 Issue 2, p1247-1261, 15p
- Publication Year :
- 2022
-
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 / (π N). As a consequence, we prove strong laws and a limit distribution for the local time. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 08949840
- Volume :
- 35
- Issue :
- 2
- Database :
- Complementary Index
- Journal :
- Journal of Theoretical Probability
- Publication Type :
- Academic Journal
- Accession number :
- 156619957
- Full Text :
- https://doi.org/10.1007/s10959-020-01065-2