21 citations · 43 across the 7 of their papers we have counts for
8 papers · 1 filter
Large Random Simplicial Complexes, III; The Critical Dimension
A. Costa, M. Farber
In this paper we study the notion of critical dimension of random simplicial complexes in the general multi-parameter model described in our previous papers of this series. This mo…
Homological Domination in Large Random Simplicial Complexes
A. Costa, M. Farber
In this paper we state the homological domination principle for random multi-parameter simplicial complexes, claiming that the Betti number in one specific dimension (which is expl…
Random Simplicial Complexes
A. Costa, M. Farber
In this paper we introduce a new model of random simplicial complexes depending on multiple probability parameters. This model includes the well-known Linial - Meshulam random simp…
Fundamental groups of random clique complexes
Armindo Costa, Michael Farber, Danijela Horak
We study fundamental groups of clique complexes associated to random graphs. We establish thresholds for their cohomological and geometric dimension and torsion. We also show that…
Geometry and Topology of Random 2-complexes
A. E. Costa, M. Farber
We study random 2-dimensional complexes in the Linial - Meshulam model and find torsion in their fundamental groups at various regimes. We find a simple algorithmically testable cr…
Topology of random 2-complexes
Armindo Costa, Michael Farber, Thomas Kappeler
We study the Linial--Meshulam model of random two-dimensional simplicial complexes. One of our main results states that for a random 2-complex collapses simplicia…