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

Lei Yu

Given a convex function $\hat{I}¦:[0,1]\to \mathbb{R}$, the $\hat{I}¦$-stability of a Boolean function $f$ is defined as $\mathbb{E}[\hat{I}¦(T_{\ddot{I}}f(\mathbf{X}))]$, where $\mathbf{X}$ is a random vect…