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Moderate deviations for weight-dependent random connection models

Part of: Limit theorems Geometric probability and stochastic geometry Stochastic processes

Published online by Cambridge University Press:  04 June 2025

Nils Heerten ,
Christian Hirsch Open the ORCID record for Christian Hirsch [Opens in a new window]  and
Moritz Otto Open the ORCID record for Moritz Otto [Opens in a new window]
Nils Heerten*
Affiliation:
Ruhr University Bochum
Christian Hirsch*
Affiliation:
Aarhus University
Moritz Otto*
Affiliation:
Leiden University
*
*Email address: nils.heerten@rub.de
**Email address: hirsch@math.au.dk
***Email address: m.f.p.otto@math.leidenuniv.nl
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Abstract

In this paper we derive cumulant bounds for subgraph counts and power-weighted edge lengths in a class of spatial random networks known as weight-dependent random connection models. These bounds give rise to different probabilistic results, from which we mainly focus on moderate deviations of the respective statistics, but also show a concentration inequality and a normal approximation result. This involves dealing with long-range spatial correlations induced by the profile function and the weight distribution. We start by deriving the bounds for the classical case of a Poisson vertex set, and then provide extensions to α-determinantal processes.

Keywords

Moderate deviationsα-determinantal process

MSC classification

Primary: 60F10: Large deviations
Secondary: 60G55: Point processes 60D05: Geometric probability and stochastic geometry

Information

Type
Original Article
Information
Journal of Applied Probability , First View , pp. 1 - 23
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Applied Probability Trust

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