Abstract
The mean number of distinct sites visited by correlated walks on one-, two-, and three-dimensional lattices is studied by numerical simulations and by generating-function techniques. The random walks include correlations over two consecutive steps. The asymptotic behavior is derived analytically in d=1, and in d=2, 3 for the model with restricted reversals, and good agreement with the simulations is found. The model with increased probability for forward steps is studied numerically in d=2, 3 and analyzed. It is found in all cases that the mean number of visited sites cannot be simply obtained by rescaling the step number n with the correlation factor f, but there are additional correction terms that do not obey scaling.
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