Moderate deviations for weight-dependent random connection models

Journal of Applied Probability, vol. 62, pp. 1406–1428

Abstract

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.

Authors 3

1. Nils Heerten corresponding

   Ruhr University Bochum

   Affiliation as printed

   Ruhr University Bochum

2. Christian Hirsch corresponding

   Aarhus University

   Affiliation as printed

   Aarhus University

3. Moritz Otto corresponding Aachen

   Leiden University

   Affiliation as printed

   Leiden University