For fat tailed distributions, the empirical distributions does not reflect the true statistical properties, particularly for extremes. This is a simplified side note to a paper with Mark Spitznagel on why people make a mistake by looking at raw historical data as “empiricism”.

So I am fed up with academics who say “we know it is fat tails” yet not understand the consequences.

This tutorial presents the intuitions of the randomness of sample correlation (spurious correlation) and the methodologies in derivations. Some later sections are somewhat technical as Nassim rederived an old equation with more precise functions (in order to apply to fat tails) and showed the distribution of the maximum of d variables with n points per variable.
This paves the way to the real scientific work on random matric theory under fat tails and the failure of Marchenko-Pastur.