Number of distinct sites visited by random walks in lattice gases

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Abstract
The number of distinct sites visited by the correlated random walk of tagged particles in lattice gases is investigated. The lattices are occupied with concentration 0<c<1 and the particles are noninteracting except that double occupancy of lattice sites is forbidden. The distribution of the number of sites visited in one dimension and its mean value in higher dimensions d=2 and d=3 are studied by numerical simulations and analyzed in terms of scaling expressions, partly guided by heuristic models.