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

Journal of Theoretical Probability, ISSN: 1572-9230, Vol: 35, Issue: 2, Page: 1247-1261
2022
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Metric Options:   Counts1 Year3 Year

Metrics Details

  • Citations
    2
    • Citation Indexes
      2

Article Description

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 / (πN). As a consequence, we prove strong laws and a limit distribution for the local time.

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