Emanuel Milman

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math.FA2026

Thin-Shell implies small-ball deviation via Gaussian tilts

Silouanos Brazitikos, Emanuel Milman

We show that uniform thin-shell estimates for (even) isotropic log-concave measures $μ$ on $R^{n}$ yield precise and explicit deviation estimates for the Euclidean norm $|X|…

math.FA2026

The Gaussian Conjugate Rogers-Shephard Inequality

Emanuel Milman, Shohei Nakamura, Hiroshi Tsuji

We fuse between the Rogers-Shephard inequality for the Lebesgue measure and Royen's Gaussian Correlation Inequality, simultaneously extending both into a single sharp inequality fo…

math.FA2025

Gaussian Correlation via Inverse Brascamp-Lieb

Emanuel Milman

We give a simple alternative proof of Royen's Gaussian Correlation inequality by using (a slightly generalized version of) Nakamura-Tsuji's symmetric inverse Brascamp-Lieb inequali…

math.FA2025

A Blaschke-SantalÃ³ inequality for unconditional log-concave measures

Emanuel Milman, Amir Yehudayoff

The Blaschke-SantalÃ³ inequality states that the volume product $∣ K ∣ \cdot ∣ K^{o} ∣$ of a symmetric convex body $K \subset R^{n}$ is maximized by the standard Euclidean unit-…

math.FA2025

Fixed and Periodic Points of the Intersection Body Operator

Emanuel Milman, Shahar Shabelman, Amir Yehudayoff

The intersection body $I K$ of a star-body $K$ in $R^{n}$ was introduced by E. Lutwak following the work of H. Busemann, and plays a central role in the dual Brunn-Minkowski…