On the Area of the Largest Square Covered by a Comb-Random-Walk

  • Pal RévészEmail author
Part of the Fields Institute Communications book series (FIC, volume 76)


We study the path behaviour of a simple random walk C on the 2-dimensional comb lattice that is obtained from \(\mathbb{Z}^{2}\) by removing all horisontal edges off the X-axis. We say that a lattice point is covered by C at time n if there is a k ≤ n for which C(k) = (x, y). A set A is covered if each (x, y) ∈ A is covered. Let R n be the largest integer for which [−R n , R n ]2 is covered at time n. Our main result gives an upper and a lower bound for R n . A similar question is investigated for a random walk on the half-plane half-comb lattice.



Research supported by Hungarian Research Grant OTKA K108615.


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Technische Universitët WienInstitut für StatistikWienAustria

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