Large random simplicial complexes, III the critical dimension

DOI10.1142/S0218216517400107zbMath1367.55011arXiv1512.08714MaRDI QIDQ2969704

Michael S. Farber, A. E. Costa

Publication date: 23 March 2017

Published in: Journal of Knot Theory and Its Ramifications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1512.08714

zbMATH Keywords

Betti numbercritical dimensionrandom simplicial complex

Mathematics Subject Classification ID

Random graphs (graph-theoretic aspects) (05C80) Random matrices (probabilistic aspects) (60B20) Random matrices (algebraic aspects) (15B52) Simplicial sets and complexes in algebraic topology (55U10)

Related Items (20)

Large random simplicial complexes, II; the fundamental group ⋮ Random recursive hypergraphs ⋮ Random Simplicial Complexes: Models and Phenomena ⋮ Random simplicial complexes, duality and the critical dimension ⋮ Maps on random hypergraphs and random simplicial complexes ⋮ Simplicial SIR rumor propagation models with delay in both homogeneous and heterogeneous networks ⋮ Topological embeddings into random 2‐complexes ⋮ Law of large numbers for Betti numbers of homogeneous and spatially independent random simplicial complexes ⋮ Algebraic and combinatorial expansion in random simplicial complexes ⋮ The homology of random simplicial complexes in the multi-parameter upper model ⋮ Large deviations for subcomplex counts and Betti numbers in multiparameter simplicial complexes ⋮ Homology of multi-parameter random simplicial complexes ⋮ What Are Higher-Order Networks? ⋮ Random hypergraphs, random simplicial complexes and their Künneth-type formulae ⋮ Functional central limit theorems for local statistics of spatial birth-death processes in the thermodynamic regime ⋮ Random Simplicial Complexes ⋮ Large random simplicial complexes, I ⋮ Limit theorems for topological invariants of the dynamic multi-parameter simplicial complex ⋮ Random simplicial complexes in the medial regime ⋮ Topology of random -dimensional cubical complexes

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• Topics of Stochastic Algebraic Topology
• Fundamental groups of clique complexes of random graphs
• Large random simplicial complexes, I
• Networks

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