Before revision: For fat tailed distributions ( i.e. those that decay slower than an exponential), large deviations not only become relatively likely, but the way in which they are realized changes dramatically: A finite fraction of the whole sample deviation is concentrated on a single variable : large deviations are not the accumulation of many small deviations, but rather they are dominated to a single large fluctuation .
After revision: For fat tailed distributions ( i.e. those that decay slower than an exponential), large deviations not only become relatively likely, but they also occur in a rather peculiar way where a finite fraction of the whole sample deviation is concentrated on a single variable : large deviations are not the accumulation of many small deviations, but rather they are dominated to a single large fluctuation .