2006/05/15 by Mario Ferraro, M. Ferraro, L. Zaninetti +2 · 1 citation
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · Physics and Astronomy · #Advanced Clustering Algorithms Research #Algorithm #Artificial intelligence #Bayesian Methods and Mixture Models #Combinatorics #Computer science #Data Management and Algorithms #Data set #Diffusion and Search Dynamics #Dimension (graph theory) #Estimator #Homogeneous #Interval (graph theory) #Kernel (algebra) #Kernel density estimation #Lattice (music) #Lévy flight #Mathematical Dynamics and Fractals #Mathematical analysis #Mathematics #Monte Carlo method #Partition (number theory) #Physics #Random walk #Ranking (information retrieval) #Set (abstract data type) #Statistical physics #Statistics #Theoretical and Computational Physics #physics.data-an #physics.gen-ph
paper · pdf · doi:10.1103/physreve.73.057102
9 pages 3 figures. Accepted for publication on Physical Review E
arxiv created 2006/05/15 · openalex publication_date 2008/01/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/04/28
Formulas are derived to compute the mean number of times a site has been visited during symmetric Levy flights. Unrestricted Levy flights are considered first, for lattices of any dimension: conditions for the existence of finite asymptotic maps of the visits over the lattice are analyzed and a connection is made with the transience of the flight. In particular it is shown that flights on lattices of dimension greater than 1 are always transient. For an interval with absorbing boundaries the mean number of visits reaches stationary values, which are computed by means of numerical and analytical methods; comparisons with Monte Carlo simulations are also presented.