5 problems

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

Noise-stability conjecture for linear threshold functions.

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 $f$…

Linear-threshold correlation conjecture. If ${\cal A}$ is increasing and balanced, then there exists an increasing family ${\cal B}$ represented by a linear threshold function such…

Benjamini–Kalai–Schramm conjecture. The universal constant satisfies