A dimension-free bound for isoperimetry of unconditional log-concave measures
We prove a dimension-free Poincar\'e inequality for isotropic unconditional log-concave probability measures, establishing the Kannan-Lov\'asz-Simonovits (KLS) conjecture in the unconditional setting. The proof combines a new application of Dunkl operator theory combined with an appropriate transformation of the log-co...