Expected number of distinct sites visited by N Lvy flights on a one-dimensional lattice
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We calculate asymptotic forms for the expected number of distinct sites, [Formula Presented](n), visited by N noninteracting n-step symmetric Lvy flights in one dimension. By a Lvy flight we mean one in which the probability of making a step of j sites is proportional to 1/j[Formula Presented] in the limit j. All values of 0 are considered. In our analysis each Lvy flight is initially at the origin and both N and n are assumed to be large. Different asymptotic results are obtained for different ranges in . When n is fixed and N we find that [Formula Presented](n) is proportional to ([Formula Presented][Formula Presented] for <1 and to [Formula Presented][Formula Presented] for 1. When exceeds 2 the second moment is finite and one expects the results of Larralde et al. [Phys. Rev. A 45, 7128 (1992)] to be valid. We give results for both fixed n and N and N fixed and n. In the second case the analysis leads to the behavior predicted by Larralde et al. 1996 The American Physical Society.
author list (cited authors)
Berkolaiko, G., Havlin, S., Larralde, H., & Weiss, G. H.
complete list of authors
Berkolaiko, G||Havlin, S||Larralde, H||Weiss, GH