When Do Heavy-Tail Distributions Help? 
     N. Hansen, F. Gemperle, A. Auger, P. Koumoutsakos

Abstract.  We examine the evidence for the widespread belief that
  heavy tail distributions enhance the search for minima on multimodal
  objective functions.  We analyze isotropic and anisotropic
  heavy-tail Cauchy distributions and investigate the probability to
  sample a better solution, depending on the step length and the
  dimensionality of the search space. The probability decreases fast
  with increasing step length for isotropic Cauchy distributions and
  moderate search space dimension.  The anisotropic Cauchy
  distribution maintains a large probability for sampling large steps
  along the coordinate axes, resulting in an exceptionally good
  performance on the separable multimodal Rastrigin function.  In
  contrast, on a non-separable rotated Rastrigin function or for the
  isotropic Cauchy distribution the performance difference to a
  Gaussian search distribution is negligible.

In: Ninth International Conference on Parallel Problem Solving from
Nature PPSN IX, Proceedings, pp.62-71, Berlin: Springer, 2006.