## Abstract

We study the average number of distinct sites [formula presented] visited by Lévy flights injected in the center of a lattice: [formula presented] new particles appear in the center of the lattice at each time step. Lévy flights are particles which have the probability [formula presented] of making an [formula presented]-length jump. We show analytically that the asymptotic form of [formula presented] is related to that of the case of constant initial number [formula presented] of particles. We find that different ranges of [formula presented] correspond to different limits, [formula presented] [formula presented], in the behavior of the number of sites visited by constant number of particles. The results obtained analytically are in good agreement with Monte Carlo simulations. We also discuss possible results for [formula presented]

Original language | English |
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Pages (from-to) | 2549-2552 |

Number of pages | 4 |

Journal | Physical Review E |

Volume | 57 |

Issue number | 3 |

DOIs | |

State | Published - 1998 |