Hanson-Wright inequality and sub-gaussian concentration

Mark Rudelson, Roman Vershynin

Published 2013-06-12, updated 2013-10-01Version 3

In this expository note, we give a modern proof of Hanson-Wright inequality for quadratic forms in sub-gaussian random variables. We deduce a useful concentration inequality for sub-gaussian random vectors. Two examples are given to illustrate these results: a concentration of distances between random vectors and subspaces, and a bound on the norms of products of random and deterministic matrices.