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On limit theorems for persistent Betti numbers from dependent data. (English) Zbl 1475.60027

This paper is about very interesting Betti numbers. The aim of this paper is to provide two advances in the study of persistent Betti numbers in the context of time series and random fields. On the one hand, the author studies the large sample behavior of the expectation of persistent Betti numbers obtained from time series and random fields. On the other hand, he establishes an exponential inequality and gives strong laws of large numbers for persistent Betti numbers, which are not exclusively derived from point clouds.

MSC:

60D05 Geometric probability and stochastic geometry
60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
60F10 Large deviations
37M10 Time series analysis of dynamical systems
60G60 Random fields
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