Abstract
The problem of the covering time for sites visitedk-times is defined as the mean time taken by a random walk to visit each site of a lattice at leastk times. We performed the investigation using Monte Carlo simulations over one dimensional lattices, ofN sites, with periodic boundary conditions. Two different regions are investigated:N≫k≫1 andk≫N≫1. In the former region, we obtain a behaviour of the typet k/t 1=a ∞−Bk −0.35+A(k)N −0.75, (a ∞<1.6). In the latter region we obtain two possible behaviours:t k ∼k 0.95 andt k ∼k(lnk)−0.5. Two formulas which have a very close behaviour.
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Mirasso, C.R., Mártin, H.O. The lattice covering time problem for sites visitedk-times. Z. Physik B - Condensed Matter 82, 433–436 (1991). https://doi.org/10.1007/BF01357191
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DOI: https://doi.org/10.1007/BF01357191