A Phase Transition for the Metric Distortion of Percolation on the Hypercube

Omer Angel, Itai Benjamini

Let H_n be the hypercube {0,1}^n, and let H_{n,p} denote the same graph with Bernoulli bond percolation with parameter p=n^-α. It is shown that at α=1/2 there is a phase transition…