Limit theorems for process-level Betti numbers for sparse and critical regimes

DOI10.1017/apr.2019.50zbMath1456.60044arXiv1809.05758OpenAlexW3022728133MaRDI QIDQ3298812

Takashi Owada, Andrew M. Thomas

Publication date: 16 July 2020

Published in: Advances in Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1809.05758

zbMATH Keywords

central limit theoremBetti numberPoisson limit theoremrandom topology

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Central limit and other weak theorems (60F05) Simplicial sets and complexes in algebraic topology (55U10) Combinatorial aspects of simplicial complexes (05E45)

Related Items (9)

Limit theory for U-statistics under geometric and topological constraints with rare events ⋮ Testing goodness of fit for point processes via topological data analysis ⋮ Limit theory of sparse random geometric graphs in high dimensions ⋮ Large deviation principle for geometric and topological functionals and associated point processes ⋮ Topological data analysis of noise: uniform unimodal distributions ⋮ Strong law of large numbers for Betti numbers in the thermodynamic regime ⋮ On limit theorems for persistent Betti numbers from dependent data ⋮ Convergence of persistence diagram in the sparse regime ⋮ Functional limit theorems for the euler characteristic process in the critical regime

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