Strong law of large numbers for Betti numbers in the thermodynamic regime

DOI10.1007/s10955-018-2201-zzbMath1442.60020arXiv1805.05032OpenAlexW2903033611MaRDI QIDQ1731014

Akshay Goel, Kenkichi Tsunoda, Trinh Khanh Duy

Publication date: 6 March 2019

Published in: Journal of Statistical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1805.05032

zbMATH Keywords

manifoldsstrong law of large numbersBetti numbersrandom geometric complexesthermodynamic regime

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Strong limit theorems (60F15)

Related Items (11)

Random connection models in the thermodynamic regime: central limit theorems for add-one cost stabilizing functionals ⋮ Functional strong laws of large numbers for Euler characteristic processes of extreme sample clouds ⋮ Random Simplicial Complexes: Models and Phenomena ⋮ A limit theorem for persistence diagrams of random filtered complexes built over marked point processes ⋮ Limit theorems for process-level Betti numbers for sparse and critical regimes ⋮ Random geometric complexes and graphs on Riemannian manifolds in the thermodynamic limit ⋮ On central limit theorems in stochastic geometry for add-one cost stabilizing functionals ⋮ On the choice of weight functions for linear representations of persistence diagrams ⋮ Functional strong law of large numbers for Betti numbers in the tail ⋮ Convergence of persistence diagram in the sparse regime ⋮ Functional limit theorems for the euler characteristic process in the critical regime

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