  In this paper, we consider accessibility percolation on hypercubes, i.e., we
place i.i.d. uniform [0,1] random variables on vertices of a hypercube, and
study whether there is a path connecting two vertices such that the values of
these random variables increase along the path. We establish a sharp phase
transition depending on the difference of the values at the two endpoints, and
determine the critical window of the phase transition. Our result completely
resolves a conjecture of Berestycki, Brunet and Shi (2014).
