Gigantic random simplicial complexes

Exponential random simplicial complexes

Abstract Exponential random graph models have attracted significant research attention over the past decades. These models are maximum-entropy ensembles subject to the constraints that the expected values of a set of graph observables are equal to given values. Here we extend these maximum-entropy ensembles to random simplicial complexes, which are more adequate and versatile constructions to m...

Random Abstract Simplicial Complexes Reduction

Random abstract simplicial complex representation provides a mathematical description of wireless networks and their topology. In order to reduce the energy consumption in this type of network, we intend to reduce the number of network nodes without modifying neither the connectivity nor the coverage of the network. In this paper, we present a reduction algorithm that lower the number of points...

Random Simplicial Complexes - Around the Phase Transition

This article surveys some of the work done in recent years on random simplicial complexes. We mostly consider higher-dimensional analogs of the well known phase transition inG(n, p) theory that occurs at p = 1 n . Our main objective is to provide a more streamlined and unified perspective of some of the papers in this area.

On Topological Minors in Random Simplicial Complexes

Simplicial Complexes. A (finite abstract) simplicial complex is a finite set system that is closed under taking subsets, i.e., F ⊂ H ∈ X implies F ∈ X. The sets F ∈ X are called faces of X. The dimension of a face F is dim(F ) = |F | − 1. The dimension of X is the maximal dimension of any face. A k-dimensional simplicial complex will also be called a k-complex.

Integral Homology of Random Simplicial Complexes