Insertion-tolerance and repetitiveness of random graphs
  Bond percolation on Cayley graphs provides examples of random graphs. Other examples arise from the dynamical study of proper repetitive subgraphs of Cayley graphs. In this paper we demonstrate that these two families have mutually singular laws as a corollary of a general lemma about countable Borel equivalence relations on first countable Hausdorff spaces. 
Fernando Alcalde Cuesta, \'Alvaro Lozano Rojo, Ant\'on C. V\'azquez   Mart\'inez
math.DS