  Rayleigh-Levy flights have played a significant role in cosmology as
simplified models for understanding how matter distributes itself under
gravitational influence. These models also exhibit numerous remarkable
properties that enable the prediction of a wide range of characteristics. Here,
we derive the one and two point statistics of extreme points within
Rayleigh-Levy flights spanning one to three dimensions, stemming directly from
fundamental principles. In the context of the mean field limit, we provide
straightforward closed-form expressions for Euler counts and their
correlations, particularly in relation to their clustering behaviour over long
distances. Additionally, quadratures allow for the computation of extreme value
number densities. A comparison between theoretical predictions in 1D and Monte
Carlo measurements shows remarkable agreement. Given the widespread use of
Rayleigh-Levy processes, these comprehensive findings offer significant promise
not only in astrophysics but also in broader applications beyond the field.
