First Passage Percolation Has Sublinear Distance Variance

Itai Benjamini, Gil Kalai, Oded Schramm

Let $0<a<b<\infty$, and for each edge $e$ of $Z^d$ let ${\omega }_e=a$ or ${\omega }_e=b$, each with probability 1/2, independently. This induces a random metric $\dist_ω$ on the vertices of $Z^d$…