4 problems

Let $f:(\{0,1\}^n,\mu_{1/2}^n)\to\{\pm1\}$ be Boolean-valued, with spectral entropy … and total influence ${\rm I}^{(1/2)}[f]=\sum_{i=1}^n{\rm Inf}_i^{(1/2)}[f]$. Friedgut–Kalai's…

Directed KKL inequality. Given a Boolean function $f\colon\{0,1\}^n\to\{0,1\}$, there exists $i\in[n]$ such that

Let $K \subseteq \mathbb{R}^n$ be symmetric and convex, and let $v \in \mathbb{S}^{n-1}$ satisfy $\operatorname{Inf}_v[K] \leq \varepsilon$. A symmetric convex set $L$ can be compa…

Aaronson–Ambainis conjecture. Every such function satisfies