Large Deviations Of Sums Mainly Due To Just One Summand

Abstract

We present a formalization of the well-known thesis that, in the case of independent identically distributed random variables $X_1,\dots ,X_n$ with power-like tails of index $\alpha \in (0,2)$, large deviations of the sum $X_1+\cdots +X_n$ are primarily due to just one of the summands.

6 pages; to appear in The American Mathematical Monthly