Remarks on the Most Informative Function Conjecture at fixed mean

Guy Kindler, Ryan O'Donnell, David Witmer

In 2013, Courtade and Kumar posed the following problem: Let $\mathbf{x}\sim \{\pm 1{\}}^n$ be uniformly random, and form $\mathbf{y}\sim \{\pm 1{\}}^n$ by negating each bit…