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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 isotropic log-concave measures on yield precise and explicit deviation estimates for the Euclidean norm below…
math.SP2026
Spectral and Isoperimetric Bounds on Flat Tori
Emanuel Milman
We record several elementary relations between spectral and isoperimetric parameters of a flat torus and the covariance structure of a fundamental do…
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…