On the $\Phi$-Stability and Related Conjectures

Lei Yu

Given a convex function $\Phi :[0,1]\to \mathbb{R}$ and the mean $\mathbb{E}f(\mathbf{X})=a\in [0,1]$, which Boolean function $f$ maximizes the $\Phi$-stability $\mathbb{E}[Φ(T_ρf(\mathbf{X…