B. Letwin

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math.MG2026

Dimension-free Gaussian tail estimates for linear functionals on convex bodies

Brayden Letwin, Dan Mikulincer

Let $K \subset R^{n}$ be a centered convex body of volume one. We prove that there exist absolute constants $c, C > 0$ and an orthonormal set of vectors $I^ \subset S^{n - 1}$ w…

math.MG2024

A generalization of GrÃ¼nbaum's inequality

Brayden Letwin, Vladyslav Yaskin

GrÃ¼nbaum's inequality gives sharp bounds between the volume of a convex body and its part cut off by a hyperplane through the centroid of the body. We provide a generalization of…