Levy flights (LFs), also
referred to as Levy motion, stand for a class of non-Gaussian Markovian
random processes whose stationary increments are distributed according
to a Levy stable distribution originally studied by the French
mathematician Paul Pierre Levy. Levy stable laws are important because
of three fundamental properties: (i) Similar to the Gaussian law, Levy
stable laws form the basin of attraction for sums of random variables.
(ii) The probability density functions of Levy stable laws decay in
asymptotic power-law form with diverging variance and thus appear
naturally in the description of many fluctuation processes
with scattering statistics characterized by bursts or large
outliers; (iii) LFs are statistically self-affine, a property used for
the description of random fractal processes. Here we briefly
review the fundamental properties of LFs.