Analyticity of the percolation density $\theta$ in all dimensions

Abstract

We prove that for Bernoulli bond percolation on ${\mathbb{Z}}^d$, $d\ge 2$ the percolation density is an analytic function of the parameter in the supercritical interval $(p_c,1]$. This answers a question of Kesten from 1981.

Appearing in Memoirs of the AMS as part of arxiv:1811.07404