# Cohomology groups of non-uniform random simplicial complexes

## Main Article Content

## Abstract

We consider a model of a random simplicial complex generated by takingthe downward-closure of a non-uniform binomial random hypergraph, in whicheach set of k+1 vertices forms an edge with some probability pk independently,where pk depends on k and on the number of vertices n. We consider a notion of connectednesson this model according to the vanishing of cohomology groups over an arbitrary abelian group R. We prove that this notionof 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.

## Article Details

How to Cite

Cooley, O., Del Giudice, N., Kang, M., & Sprüssel, P.
(2019).
Cohomology groups of non-uniform random simplicial complexes.

*Acta Mathematica Universitatis Comenianae, 88*(3), 553-560. Retrieved from http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/1288/693
Issue

Section

EUROCOMB 2019