5 problems

Let $X$ be uniformly distributed on $\{0,1\}^n$, let $Y$ be obtained from $X$ through a memoryless binary symmetric channel with crossover probability $0<p<\frac{1}{2}$, and let…

Let $f:\{0,1\}^n\to\{\pm 1\}$ be balanced, meaning that $\mathbf{E}f=0$. For $\rho\in[-1,1]$, let $T_\rho f$ denote the standard noise operator applied to $f$. Hellinger conjecture…

The Hellinger conjecture. Under these assumptions,

Let $X$ be uniformly distributed on $\{0,1\}^n$, let $Y$ be obtained from $X$ through a binary symmetric channel with crossover probability $0<p<\frac{1}{2}$, and let…

Let $X$ be uniformly distributed on $\{0,1\}^n$, let $Y$ be obtained from $X$ through a binary symmetric channel with crossover probability $0<p<\frac{1}{2}$, and let…