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Hermite-Fisher bounds and stability for min-entropy power inequalities
Abstract
We derive explicit lower bounds for relative Fisher information by combining a variational principle with suitably orthogonalized Hermite-polynomial test functions. The resulting cumulant bounds are asymptotically sharp and yield lower bounds for Gaussian entropy deficits. We also establish quantitative versions of sharp min-entropy power inequalities in all dimensions. En route, we develop a stability result for Brzezinski's sharp bound for block sections of products of Euclidean balls, which may be of independent interest.
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BibTeX
@misc{brazitikos2026hermitefisher,
title = {{Hermite-Fisher bounds and stability for min-entropy power inequalities}},
author = {Silouanos Brazitikos and Martin Rapaport and Tomasz Tkocz},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.22065},
eprint = {2609.22065},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.22065},
}
RIS
TY - UNPB
TI - Hermite-Fisher bounds and stability for min-entropy power inequalities
AU - Silouanos Brazitikos
AU - Martin Rapaport
AU - Tomasz Tkocz
PY - 2026
DA - 2026/09/18
PB - arXiv
DO - 10.48550/arxiv.2609.22065
UR - https://arxiv.org/abs/2609.22065
AB - We derive explicit lower bounds for relative Fisher information by combining a variational principle with suitably orthogonalized Hermite-polynomial test functions. The resulting cumulant bounds are asymptotically sharp and yield lower bounds for Gaussian entropy deficits. We also establish quantitative versions of sharp min-entropy power inequalities in all dimensions. En route, we develop a stability result for Brzezinski's sharp bound for block sections of products of Euclidean balls, which may be of independent interest.
ER -