PreprintCC BY 4.0arXiv
A Gaussian Chain Rule Proof of the Banach Space Hanson Wright Bound
Abstract
For a finite family of real matrices, we bound the Gaussian width of the union of its image ellipsoids by its maximal Hilbert Schmidt norm, its maximal fixed input Gaussian width, and the square root of the product of its operator radius and decoupled Gaussian chaos supremum.
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BibTeX
@misc{bednorz2026gaussian,
title = {{A Gaussian Chain Rule Proof of the Banach Space Hanson Wright Bound}},
author = {Witold Bednorz and Rafal Martynek and Rafal Meller},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.23147},
eprint = {2609.23147},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.23147},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A Gaussian Chain Rule Proof of the Banach Space Hanson Wright Bound
AU - Witold Bednorz
AU - Rafal Martynek
AU - Rafal Meller
PY - 2026
DA - 2026/09/19
PB - arXiv
DO - 10.48550/arxiv.2609.23147
UR - https://arxiv.org/abs/2609.23147
AB - For a finite family of real matrices, we bound the Gaussian width of the union of its image ellipsoids by its maximal Hilbert Schmidt norm, its maximal fixed input Gaussian width, and the square root of the product of its operator radius and decoupled Gaussian chaos supremum.
ER -