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arXiv · 2609.22065

Hermite-Fisher bounds and stability for min-entropy power inequalities

Silouanos Brazitikos·Martin Rapaport·Tomasz Tkocz
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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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Silouanos Brazitikos, Martin Rapaport, Tomasz Tkocz. 2026-09-18. Hermite-Fisher bounds and stability for min-entropy power inequalities. https://arxiv.org/abs/2609.22065

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