Hanson-Wright inequality and sub-gaussian concentration

Mark Rudelson; Roman Vershynin

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arXiv · 1306.2872

Hanson-Wright inequality and sub-gaussian concentration

Mark Rudelson·Roman Vershynin

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Abstract

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.

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Mark Rudelson, Roman Vershynin. 2013-10-01. Hanson-Wright inequality and sub-gaussian concentration. https://arxiv.org/abs/1306.2872

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