---
res:
bibo_abstract:
- "We consider a generalised model of a random simplicial complex, which arises
from a random hypergraph. Our model is generated by taking the downward-closure
of a non-uniform binomial random hypergraph, in which for each k, each set of
k+1 vertices forms an edge with some probability pk independently. As a special
case, this contains an extensively studied model of a (uniform) random simplicial
complex, introduced by Meshulam and Wallach [Random Structures & Algorithms 34
(2009), no. 3, pp. 408–417].\r\nWe consider a higher-dimensional notion of connectedness
on this new 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. In addition, we determine the asymptotic behaviour of cohomology groups
inside the critical window around the time of the phase transition.@eng"
bibo_authorlist:
- foaf_Person:
foaf_givenName: Oliver
foaf_name: Cooley, Oliver
foaf_surname: Cooley
foaf_workInfoHomepage: http://www.librecat.org/personId=43f4ddd0-a46b-11ec-8df6-ef3703bd721d
- foaf_Person:
foaf_givenName: Nicola
foaf_name: Del Giudice, Nicola
foaf_surname: Del Giudice
- foaf_Person:
foaf_givenName: Mihyun
foaf_name: Kang, Mihyun
foaf_surname: Kang
- foaf_Person:
foaf_givenName: Philipp
foaf_name: Sprüssel, Philipp
foaf_surname: Sprüssel
bibo_doi: 10.37236/10607
bibo_issue: '3'
bibo_volume: 29
dct_date: 2022^xs_gYear
dct_identifier:
- UT:000836200300001
dct_isPartOf:
- http://id.crossref.org/issn/1077-8926
dct_language: eng
dct_publisher: Electronic Journal of Combinatorics@
dct_title: Phase transition in cohomology groups of non-uniform random simplicial
complexes@
...