Limit theorems for point processes under geometric constraints (and topological crackle)

DOI10.1214/16-AOP1106zbMath1373.60090arXiv1503.08416OpenAlexW2964131216MaRDI QIDQ2012256

Robert J. Adler, Takashi Owada

Publication date: 28 July 2017

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1503.08416

zbMATH Keywords

regular variationpoint processgeometric graphextreme value theoryBetti numbertopological data analysisPoisson random measureČech complexcrackle

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Extreme value theory; extremal stochastic processes (60G70) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

Related Items (17)

Geometric and probabilistic limit theorems in topological data analysis ⋮ Topology of random geometric complexes: a survey ⋮ Limit theorems for persistence diagrams ⋮ Limit theorems for Betti numbers of extreme sample clouds with application to persistence barcodes ⋮ Functional strong laws of large numbers for Euler characteristic processes of extreme sample clouds ⋮ Extremal lifetimes of persistent cycles ⋮ Homological connectivity in random Čech complexes ⋮ Convergence of persistence diagrams for topological crackle ⋮ Poisson process approximation under stabilization and Palm coupling ⋮ Bootstrapping persistent Betti numbers and other stabilizing statistics ⋮ Large deviation principle for geometric and topological functionals and associated point processes ⋮ Asymptotics of lower dimensional zero-density regions ⋮ Random Čech complexes on Riemannian manifolds ⋮ Thresholds for vanishing of `isolated' faces in random Čech and Vietoris-Rips complexes ⋮ Probabilistic convergence and stability of random mapper graphs ⋮ Topological crackle of heavy-tailed moving average processes ⋮ Functional strong law of large numbers for Betti numbers in the tail

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