%A Cooley, Oliver
%A Del Giudice, Nicola
%A Kang, Mihyun
%A SprÃ¼ssel, Philipp
%D 2019
%T Cohomology groups of non-uniform random simplicial complexes
%K
%X We consider a model of a random simplicial complex generated by taking the downward-closure of a non-uniform binomial random hypergraph, in which each set of k+1 vertices forms an edge with some probability p k independently, where p k depends on k and on the number of vertices n. We consider a notion of connectedness on this model according to the vanishing of cohomology groups over an arbitrary abelian group R. We prove that this notion of connectedness displays a phase transition and determine the threshold. We also prove a hitting time result for a natural process interpretation, in which simplices and their downward-closure are added one by one.
%U http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/1288
%J Acta Mathematica Universitatis Comenianae
%0 Journal Article
%P 553-560%V 88
%N 3
%@ 0862-9544
%8 2019-07-26