Electronic Communications in Probability

Hanson-Wright inequality and sub-gaussian concentration

Mark Rudelson and Roman Vershynin

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

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

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subgaussian random variables measure concentration

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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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