2 problems

Kalai–Keller–Mossel correlation conjecture. For every increasing and balanced family $\mathcal{A}\subseteq\Omega_n$, there exists an increasing linear-threshold family…

Let $f\colon\{-1,1\}^{n}\rightarrow\{-1,1\}$ be a linear threshold function, with $n$ odd. For $\rho\in[0,1]$, let $\operatorname{Stab}_{\rho}[f]$ denote the noise stability of $f$…