Number of distinct sites visited by N random walkers.

@article{Larralde1992NumberOD,
  title={Number of distinct sites visited by N random walkers.},
  author={Larralde and Trunfio and Havlin and Stanley and Weiss},
  journal={Physical review. A, Atomic, molecular, and optical physics},
  year={1992},
  volume={45 10},
  pages={
          7128-7138
        }
}
  • Larralde, Trunfio, +2 authors Weiss
  • Published 1992
  • Physics, Medicine
  • Physical review. A, Atomic, molecular, and optical physics
  • We study the number of distinct sites visited by N random walkers after t steps Siv(t) under the condition that all the walkers are initially at the origin. We derive asymptotic expressions for the mean number of distinct sites (Siv(t)) in one, two, and three dimensions. We find that (Siv(t)) passes through several growth regimes; at short times (Siv(t)) ~ t" (regime I), for t» & t & t'„we find that (Siv(t)) ~ (t ln[N Si(t)/t ])" (regime II), and for t & t'„,(Siv(t)) ~ NSi(t) (regime III). The… CONTINUE READING
    68 Citations

    Figures and Tables from this paper.

    Number of common sites visited by N random walkers.
    • S. Majumdar, M. Tamm
    • Mathematics, Physics
    • Physical review. E, Statistical, nonlinear, and soft matter physics
    • 2012
    • 8
    • PDF
    Record statistics for multiple random walks.
    • 27
    • PDF
    Order statistics of Rosenstock's trapping problem in disordered media.
    • S. B. Yuste, L. Acedo
    • Mathematics, Medicine
    • Physical review. E, Statistical, nonlinear, and soft matter physics
    • 2003
    • 5
    • PDF
    Multiparticle trapping problem in the half-line
    • 9
    • PDF

    References

    SHOWING 1-3 OF 3 REFERENCES
    An Introduction to Mathematical Ecology.
    • 2,182
    An Introduction to Probability Theory and Its Applications
    • 22,105
    DIFFUSION-CONTRO LLED REACTIONS
    • 1