Geodesic
Cohomology groups of non-uniform random simplicial complexes
Oliver Cooley1 ; Nicola Del Giudice1 ; Mihyun Kang1 ; Philipp Sprüssel1 ; Oliver Cooley ; Nicola Del Giudice ; Mihyun Kang ; Philipp Sprüssel
1Graz University of Technology, Institute of Discrete Mathematics, Graz, Austria
Acta mathematica Universitatis Comenianae, Tome 88 (2019) no. 3, pp. 553-560 
Oliver Cooley; Nicola Del Giudice; Mihyun Kang; Philipp Sprüssel; Oliver Cooley; Nicola Del Giudice; Mihyun Kang; Philipp Sprüssel. Cohomology groups of non-uniform random simplicial complexes. Acta mathematica Universitatis Comenianae, Tome 88 (2019) no. 3, pp. 553-560. http://geodesic.mathdoc.fr/item/AMUC_2019_88_3_a31/
@article{AMUC_2019_88_3_a31,
     author = {Oliver Cooley and Nicola Del Giudice and Mihyun Kang and Philipp Spr\"ussel and Oliver Cooley and Nicola Del Giudice and Mihyun Kang and Philipp Spr\"ussel},
     title = { Cohomology groups of non-uniform random simplicial complexes},
     journal = {Acta mathematica Universitatis Comenianae},
     pages = {553--560},
     year = {2019},
     volume = {88},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2019_88_3_a31/}
}
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Voir la notice de l'article provenant de la source Comenius University

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.