On the local time of the Half-Plane Half-Comb walk
Probability
2020-12-14 v2
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). As15 pag a consequence we prove strong laws and a limit distribution for the local time.
Keywords
Cite
@article{arxiv.2009.11767,
title = {On the local time of the Half-Plane Half-Comb walk},
author = {Endre Csaki and Antonia Foldes},
journal= {arXiv preprint arXiv:2009.11767},
year = {2020}
}
Comments
15 pages