[Zurück]

P. Révész:
"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. (Hrg.); Springer New York, Chapter Asymptotic Laws and Methods in Stochastics Volume 76 of the series Fields Institute Communications pp 77-85, 2015, ISBN: 978-1-4939-3076-0, S. 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.

http://dx.doi.org/10.1007/978-1-4939-3076-0_5

http://link.springer.com/chapter/10.1007%2F978-1-4939-3076-0_5