Abstract
We study the territory covered by N Lévy flights by calculating the mean number of distinct sites, 〈(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 A to perform an ℓ-length jump in a randomly chosen direction at each time step. We obtain asymptotic results for different values of α. For d=2 and N→∞ we find 〈(n)〉∝, when α<2 and 〈(n)〉∝, when α>2. For d=2 and n→∞ we find 〈(n)〉∝Nn for α<2 and 〈(n)〉∝Nn/ln n for α>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 〈(n)〉 on d⩾3 dimensional lattices.
- Received 19 September 1996
DOI:https://doi.org/10.1103/PhysRevE.55.1395
©1997 American Physical Society