Sub-Gaussian distribution

Summary

A real random variable is sub-Gaussian when its tails decay at least as fast as those of a normal distribution, that is, like $e^{-c t^2}$. Normal variables and bounded variables are sub-Gaussian. Sums of independent sub-Gaussian variables are again sub-Gaussian, with explicit constants, and this gives concentration bounds of Hoeffding type. The notion is central in high-dimensional probability, random matrix theory and statistical learning.