Author

Silouanos Brazitikos

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Preprint Sep 2026

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

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 sha...

Silouanos Brazitikos, M. Rapaport, Tomasz Tkocz · 0 citations

Preprint Aug 2026

Many Facets in Random Polytopes from Product and Log-Concave Measures

We prove bounds of order $n^{n/2}e^{O(n)}$ for the expected number of facets of high-dimensional random polytopes. First, let $\mu$ be a non-degenerate compactly supported even probability measure on $\R$ satisfying $\mu([x^\ast-s,x^\ast])\asymp s^\kappa$ near its right endpoint $x^\ast$. For every sufficiently small f...

Silouanos Brazitikos, Minas Pafis · 0 citations