## Electronic Communications in Probability

### Hanson-Wright inequality and sub-gaussian concentration

#### 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.

#### Article information

Source
Electron. Commun. Probab., Volume 18 (2013), paper no. 82, 9 pp.

Dates
Accepted: 23 October 2013
First available in Project Euclid: 7 June 2016

https://projecteuclid.org/euclid.ecp/1465315621

Digital Object Identifier
doi:10.1214/ECP.v18-2865

Mathematical Reviews number (MathSciNet)
MR3125258

Zentralblatt MATH identifier
1329.60056

Rights

#### Citation

Rudelson, Mark; Vershynin, Roman. Hanson-Wright inequality and sub-gaussian concentration. Electron. Commun. Probab. 18 (2013), paper no. 82, 9 pp. doi:10.1214/ECP.v18-2865. https://projecteuclid.org/euclid.ecp/1465315621

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