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math.PR2026
A dimension-free bound for isoperimetry of unconditional log-concave measures
Dan Mikulincer, Ilias Zadik
We prove a dimension-free Poincaré inequality for isotropic unconditional log-concave probability measures, establishing the Kannan-Lovász-Simonovits (KLS) conjecture in the uncond…
math.PR2026
A Bayesian Proof of the Bernoulli Theorem
Jingbo Liu, Ilias Zadik
We give a new proof of the Bernoulli theorem, conjectured by Talagrand and proved in the seminal work of Bednorz and Latała. Our approach is based on information-theoretic ideas: l…