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The lattice covering time problem for sites visitedk-times

Research paper by Claudio R. Mirasso, Héctor O. Mártin

Indexed on: 01 Oct '91Published on: 01 Oct '91Published in: Zeitschrift für Physik B Condensed Matter



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 typetk/t1=a∞−Bk−0.35+A(k)N−0.75, (a∞<1.6). In the latter region we obtain two possible behaviours:tk∼k0.95 andtk∼k(lnk)−0.5. Two formulas which have a very close behaviour.