Territory covered by N Lévy flights on d-dimensional lattices
نویسندگان
چکیده
We study the territory covered by N Lévy flights by calculating the mean number of distinct sites, ^SN(n)&, visited after n time steps on a d-dimensional, d>2, lattice. The Lévy flights are initially at the origin and each has a probability Al 2(d1a) to perform an l -length jump in a randomly chosen direction at each time step. We obtain asymptotic results for different values of a . For d52 and N→` we find ^SN(n)& }CaN n, when a,2 and ^SN(n)&}N n, when a.2. For d52 and n→` we find ^SN(n)&}Nn for a,2 and ^SN(n)&}Nn/lnn for a.2. The last limit corresponds to the result obtained by Larralde et al. @Phys. Rev. A 45, 7128 ~1992!# for bounded jumps. We also present asymptotic results for ^SN(n)& on d>3 dimensional lattices. @S1063-651X~97!04102-0#
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