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Dimension-free KLS Poincare bound for isotropic log-concave densities (smooth compactly supported tests)

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Palomar Registrypalomar/PALOMAR-2026-11-01-000014Nov 1, 2026math.PRscore 0

A Lean 4 / Mathlib library for Poincare inequalities, log-concave probability measures and stochastic localization. Its dimension-free KLS theorem bounds the intrinsic local-slope Poincare constant by one universal constant times the covariance operator norm, including dimension zero and singular affine supports, for log-concave probability laws with finite second moment. The proof follows Bizeul-Klartag-Lehec through finite-horizon cutoff localization, the compact Letwin constant-8 quadratic variance bound and approximation. Supporting results include Cheeger-Buser comparisons, covariance…

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