This lovely term is more affectionately known by statisticians as "fat tails", and describes probability distributions that assign more liklihood to extreme rare events.
There is a veritable ocean of literature regarding this subject, and the REcapitulator, as always, directs the diligent reader to the excellent SSRN site for further reading:
However, the REcapitulator would like to make a somewhat narrow comment. A normal distribution, or even most of the distributions that exhibit "fat tails" make the assumption that VARIANCE, the spread of possible values in relation to the expected value of a given variable, is STABLE. This is not true, as volatility in markets (as measured by the VIX) is also volatile.
If we have a normal distribution, we should also expect to see an additive generator of random variables.
But this is not what we actually see. In periods of high volatility, the generator is multiplicative.
In other words, whenever you see any statistic in markets that has a normal distribution as its intellectual lynchpin, be very skeptical of any conclusions derived therefrom.