Territory covered by N Levy flights on d-dimensional lattices Academic Article uri icon


  • We study the territory covered by N Lvy flights by calculating the mean number of distinct sites, [formula presented](n), visited after n time steps on a d-dimensional, d2, lattice. The Lvy flights are initially at the origin and each has a probability A[formula presented] to perform an -length jump in a randomly chosen direction at each time step. We obtain asymptotic results for different values of . For d=2 and N we find [formula presented](n)[formula presented][formula presented][formula presented], when <2 and [formula presented](n)[formula presented][formula presented], when >2. For d=2 and n we find [formula presented](n)Nn for <2 and [formula presented](n)Nn/ln n for >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 [formula presented](n) on d3 dimensional lattices. 1997 The American Physical Society.

published proceedings


author list (cited authors)

  • Berkolaiko, G., & Havlin, S.

citation count

  • 22

complete list of authors

  • Berkolaiko, G||Havlin, S

publication date

  • February 1997