Open Access
2017 Functional central limit theorem for subgraph counting processes
Takashi Owada
Electron. J. Probab. 22: 1-38 (2017). DOI: 10.1214/17-EJP30


The objective of this study is to investigate the limiting behavior of a subgraph counting process built over random points from an inhomogeneous Poisson point process on $\mathbb R^d$. The subgraph counting process we consider counts the number of subgraphs having a specific shape that exist outside an expanding ball as the sample size increases. As underlying laws, we consider distributions with either a regularly varying tail or an exponentially decaying tail. In both cases, the nature of the resulting functional central limit theorem differs according to the speed at which the ball expands. More specifically, the normalizations in the central limit theorems and the properties of the limiting Gaussian processes are all determined by whether or not an expanding ball covers a region - called a weak core - in which the random points are highly densely scattered and form a giant geometric graph.


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Takashi Owada. "Functional central limit theorem for subgraph counting processes." Electron. J. Probab. 22 1 - 38, 2017.


Received: 11 February 2016; Accepted: 26 January 2017; Published: 2017
First available in Project Euclid: 15 February 2017

zbMATH: 1357.60056
MathSciNet: MR3622887
Digital Object Identifier: 10.1214/17-EJP30

Primary: 60D05 , 60G70
Secondary: 60G15 , 60G18

Keywords: Extreme value theory , functional central limit theorem , geometric graph , regular variation , von-Mises function

Vol.22 • 2017
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