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.
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Nemirovsky et al. (1990) studied this question.
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