Unlacing hypercube percolation : a survey

The purpose of this note is twofold. First, we survey the study of the percolation phase transition on the Hamming hypercube {0,1}^m obtained in the series of papers (Borgs et al. in Random Struct Algorithms 27:137–184, 2005; Borgs et al. in Ann Probab 33:1886–1944, 2005; Borgs et al. in Combinatorica 26:395–410, 2006; van der Hofstad and Nachmias in Hypercube percolation, Preprint 2012). Secondly, we explain how this study can be performed without the use of the so-called "lace expansion" technique. To that aim, we provide a novel simple proof that the triangle condition holds at the critical probability.