title: Lévy flights with power-law absorption.
abstract: We consider a particle performing a stochastic motion on a one-dimensional lattice with jump lengths distributed according to a power law with exponent μ+1. Assuming that the walker moves in the presence of a distribution a(x) of targets (traps) depending on the spatial coordinate x, we study the probability that the walker will eventually find any target (will eventually be trapped). We focus on the case of power-law distributions a(x)∼x(-α) and we find that, as long as μ<α, there is a finite probability that the walker will never be trapped, no matter how long the process is. This result is shown via analytical arguments and numerical simulations which also evidence the emergence of slow searching (trapping) times in finite-size system. The extension of this finding to higher-dimensional structures is also discussed.
authors.affiliation: Scuola Normale Superiore, Pisa, Italy.
authors.forename: Luca
authors.initials: L
authors.lastname: Cattivelli
authors.affiliation: Dipartimento di Matematica, Sapienza Università di Roma, Rome, Italy.
authors.forename: Elena
authors.initials: E
authors.lastname: Agliari
authors.affiliation: Max Planck Institute for Brain Research, Frankfurt, Germany.
authors.forename: Fabio
authors.initials: F
authors.lastname: Sartori
authors.affiliation: Dipartimento di Fisica, Università di Parma, Parma, Italy.
authors.forename: Davide
authors.initials: D
authors.lastname: Cassi
mesh_terms: D065966:Absorption, Physicochemical; D004058:Diffusion; D008962:Models, Theoretical; D011336:Probability; D013269:Stochastic Processes