Repository: Freie Universit├Ąt Berlin, Math Department

On the concentration of subgaussian vectors and positive quadratic forms in Hilbert spaces

Mollenhauer, Mattes and Schillings, Claudia (2023) On the concentration of subgaussian vectors and positive quadratic forms in Hilbert spaces. arXiv . (Submitted)

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Official URL: https://doi.org/10.48550/arXiv.2306.11404

Abstract

In these notes, we investigate the tail behaviour of the norm of subgaussian vectors in a Hilbert space. The subgaussian variance proxy is given as a trace class operator, allowing for a precise control of the moments along each dimension of the space. This leads to useful extensions and analogues of known Hoeffding-type inequalities and deviation bounds for positive random quadratic forms. We give a straightforward application in terms of a variance bound for the regularisation of statistical inverse problems.

Item Type:Article
Subjects:Mathematical and Computer Sciences > Mathematics > Applied Mathematics
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics > Deterministic and Stochastic PDEs Group
ID Code:3093
Deposited By: Ulrike Eickers
Deposited On:19 Feb 2024 13:50
Last Modified:19 Feb 2024 13:50

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