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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.FA2026
A Deterministic Proof of the Slicing Theorem
Silouanos Brazitikos
We give a deterministic proof of Bourgain's slicing theorem. The proof uses neither stochastic localization nor stochastic calculus, does not rely on Guan's covariance bound, and a…