Thresholds for families of multisets, with an application to graph   pebbling
  In this paper we prove two multiset analogs of classical results. We prove a multiset analog of Lovasz's version of the Kruskal-Katona Theorem and an analog of the Bollobas-Thomason threshold result. As a corollary we obtain the existence of pebbling thresholds for arbitrary graph sequences. In addition, we improve both the lower and upper bounds for the `random pebbling' threshold of the sequence of paths. 
Airat Bekmetjev, Graham Brightwell, Andrzej Czygrinow and Glenn   Hurlbert