Phys. Rev. A 41, 761–767 (1990)Universality in the lattice-covering time problemReceived 2 August 1989; published in the issue dated January 1990 The lattice-covering time t is the expected time a random walk (RW) takes to visit all N lattice sites. Regular D-dimensional lattices with periodic and reflecting boundary conditions are considered. When D=1 these covering problems are equivalent to those of the first-visit type and they can be exactly solved. In contrast, when D≥2 the lattice-covering time problems are not reducible to any known lattice RW problem. The asymptotic (N→∞) behavior of t is studied using Monte Carlo methods and interesting questions regarding universality in the covering time problem are discussed. © 1990 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevA.41.761
DOI:
10.1103/PhysRevA.41.761
PACS:
05.40.+j, 05.50.+q
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