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An $O(1)$ Bound for the KLS Constant
The Kannan--Lovász--Simonovits (KLS) conjecture asks whether every isotropic log-concave probability measure on $\mathbb R^n$ has a Cheeger constant bounded below by a universal positive constant. We prove that $ψ_n\le C$ for a universal constant $C>0$, resolving the KLS conjecture. We also prove th
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