Mean number of visits to sites in Levy flights

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.