Limit theorems for Betti numbers of random simplicial complexes
From MaRDI portal
Publication:354256
DOI10.4310/HHA.2013.v15.n1.a17zbMath1268.05180arXiv1009.4130OpenAlexW2091574535MaRDI QIDQ354256
Matthew Kahle, Elizabeth S. Meckes
Publication date: 18 July 2013
Published in: Homology, Homotopy and Applications (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1009.4130
Geometric probability and stochastic geometry (60D05) Random graphs (graph-theoretic aspects) (05C80)
Related Items
Concentration for Poisson functionals: component counts in random geometric graphs ⋮ Limit theory for U-statistics under geometric and topological constraints with rare events ⋮ Concentration for Poisson \(U\)-statistics: subgraph counts in random geometric graphs ⋮ Topology of random geometric complexes: a survey ⋮ Limit theorems for Betti numbers of extreme sample clouds with application to persistence barcodes ⋮ Networks beyond pairwise interactions: structure and dynamics ⋮ Random monomial ideals ⋮ Random Simplicial Complexes: Models and Phenomena ⋮ Intrinsic volumes of random cubical complexes ⋮ Homological connectivity in random Čech complexes ⋮ Convergence of persistence diagrams for topological crackle ⋮ Limit theory for point processes in manifolds ⋮ Hodge-Kodaira decomposition of evolving neural networks ⋮ U-Statistics in Stochastic Geometry ⋮ Robust statistics, hypothesis testing, and confidence intervals for persistent homology on metric measure spaces ⋮ Random colorings in manifolds ⋮ Large deviations for subcomplex counts and Betti numbers in multiparameter simplicial complexes ⋮ Homology of multi-parameter random simplicial complexes ⋮ On the topology of random complexes built over stationary point processes ⋮ Introduction to Stochastic Geometry ⋮ What Are Higher-Order Networks? ⋮ Clique topology reveals intrinsic geometric structure in neural correlations ⋮ Limit theory of sparse random geometric graphs in high dimensions ⋮ Large deviation principle for geometric and topological functionals and associated point processes ⋮ Asymptotics of lower dimensional zero-density regions ⋮ Random geometric complexes ⋮ Topological data analysis of noise: uniform unimodal distributions ⋮ On the one dimensional Poisson random geometric graph ⋮ Random Čech complexes on Riemannian manifolds ⋮ Strong law of large numbers for Betti numbers in the thermodynamic regime ⋮ Limit theorems for process-level Betti numbers for sparse and critical regimes ⋮ Spatiotemporal persistent homology for dynamic metric spaces ⋮ Random knots using Chebyshev billiard table diagrams ⋮ Probabilistic convergence and stability of random mapper graphs ⋮ Random geometric complexes in the thermodynamic regime ⋮ Simplicial Homology of Random Configurations ⋮ Confidence sets for persistence diagrams ⋮ Topological crackle of heavy-tailed moving average processes ⋮ Limit theorems for topological invariants of the dynamic multi-parameter simplicial complex ⋮ Crackle: the homology of noise ⋮ A persistence landscapes toolbox for topological statistics ⋮ Fréchet means for distributions of persistence diagrams ⋮ On limit theorems for persistent Betti numbers from dependent data ⋮ Unnamed Item ⋮ On the choice of weight functions for linear representations of persistence diagrams ⋮ Graph pseudometrics from a topological point of view ⋮ Functional strong law of large numbers for Betti numbers in the tail ⋮ The topology of probability distributions on manifolds ⋮ Convergence of persistence diagram in the sparse regime ⋮ Functional limit theorems for the euler characteristic process in the critical regime ⋮ Collapsibility of random clique complexes ⋮ A look into chaos detection through topological data analysis
