A phase transition for repeated averages

Sourav Chatterjee, Persi Diaconis, Allan Sly +1

Let $x_1,\dots ,x_n$ be a fixed sequence of real numbers. At each stage, pick two indices $I$ and $J$ uniformly at random and replace $x_I$, $x_J$ by $(x_I+x_J)/2$, $(x_I+x_J)/2$.…