Contributions to Books:
"On the Area of the Largest Square Covered by a Comb-Random-Walk";
in: "Asymptic Laws and Methods in Stochastics",
Volume 76, Series Part II;
D. Dawson et al. (ed.);
Springer New York,
Chapter Asymptotic Laws and Methods in Stochastics Volume 76 of the series Fields Institute Communications pp 77-85,
We study the path behaviour of a simple random walk C on the 2-dimensional comb lattice that is obtained from Z2 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.
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