Local Optimality of Dictator Functions with Applications to Courtade--Kumar and Li--Médard Conjectures

Lei Yu

Given a convex function $\Phi :[0,1]\to \mathbb{R}$, the $\Phi$-stability of a Boolean function $f$ is defined as $\mathbb{E}[\Phi (T_{\rho }f(\mathbf{X}))]$, where $\mathbf{X}$ is a random vector u…