Problem
Research questions and friction points this paper is trying to address.
relative Fisher information
min-entropy power inequalities
Hermite-polynomial test functions
Hermite-Fisher bounds and stability for min-entropy power inequalities
🤖 AI Summary
通过结合变分原理和适当正交化的Hermite多项式测试函数，本文推导出相对Fisher信息的显式下界，并建立了所有维度下的最小熵幂不等式的量化版本。
📝 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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
relative Fisher information
Hermite-polynomial test functions
min-entropy power inequalities
stability result
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