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

Mattes Mollenhauer; Claudia Schillings

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arXiv · 2306.11404

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

Mattes Mollenhauer·Claudia Schillings

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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.

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Mattes Mollenhauer, Claudia Schillings. 2023-06-20. On the concentration of subgaussian vectors and positive quadratic forms in Hilbert spaces. https://arxiv.org/abs/2306.11404

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