Random simplicial complexes - around the phase transition
  This article surveys some of the work done in recent years on random simplicial complexes. We mostly consider higher-dimensional analogs of the well known phase transition in $G(n, p)$ theory that occurs at $p = \frac 1n$ . Our main objective is to provide a more streamlined and unified perspective of some of the papers in this area. 
Nati Linial and Yuval Peled
math.CO