Topology of random simplicial complexes: a survey

By Matthew Kahle. 2013

161 citations recorded by the source corpus.

This expository article is based on a lecture from the Stanford Symposium on Algebraic Topology: Application and New Directions, held in honor of Gunnar Carlsson, Ralph Cohen, and Ib Madsen.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/94ce31282aec94b0ee1f51c6eee64b6edd66d343

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Citations in the corpus

Large random simplicial complexes, I (2015, background): “ical study of large random simplicial complexes started relatively recently and several diﬀerent probabilistic models of random topological objects have appeared within the last 10 years, see [4] and [14] for surveys. One may mention random surfaces [18], random 3-dimensional manifolds [9], random c”
Random Walks on Simplicial Complexes and the normalized Hodge Laplacian (2018, background): “Simplicial models have further been studied from a geometric perspective [17], in terms of epidemic spreading [69], or in the context of extensions of random graph models [41,73,125].”
On the topology of random complexes built over stationary point processes. (2012, methodology): “The we have the following combinatorial inequality from [23], equation (5), for k ∈ {0, .”
Random Simplicial Complexes (2014, methodology): “g curious examples of topological objects with rare combinations of topological properties. Several models of random manifolds and random simplicial complexes were suggested and studied recently, see [11] for a survey. One may mention random surfaces [15], random 3-manifodls [4], random conﬁguration”
Networks beyond pairwise interactions: structure and dynamics (2020, methodology): “To organize the rapidly growing family of models of random simplicial complexes, a model known as the “∆– ensemble” has been proposed in by Kahle [258].”
What are higher-order networks? (2021, background): “Costa and Farber [82–85] as well as Fowler [115, 116] then studied a multiparameter model, first introduced in [164], that interpolates between the Linial-Meshulam model and the random flag complex model.”
Random geometric complexes in the thermodynamic regime (2014, background): “omplex model were Random complexes 5 Yogeshwaran, Subag, Adler already investigated in [23], where a higher-dimensional version of the Erd¨osRenyi random graph model was constructed. The recent paper [19] gives a useful survey of what is known about the topology of these models, which are rather diﬀ”