4 papers · 1 filter
Central limit theorem for linear eigenvalue statistics of random geometric graphs
Christian Hirsch, Kyeongsik Nam, Moritz Otto
Random spatial networks-that is, graphs whose connectivity is governed by geometric proximity-have emerged as fundamental models for systems constrained by an underlying spatial st…
Normal and Poisson approximation for Gibbs point processes with pair potentials
Christian Hirsch, Moritz Otto, Anne Marie Svane
We provide a Poisson approximation result for dependent thinnings of Gibbs point processes as well as qualitative and quantitative central limit theorems for geometric functionals…
Functional central limit theorem for subgraph counts in a dynamic random connection model
Rajat Subhra Hazra, Nikolai Kriukov, Michel Mandjes +1
We prove a functional central limit theorem for subgraph counts in a dynamic version of the random connection model. To establish tightness, we develop a dynamic extension of the c…
Poisson approximation of large-lifetime cycles
Christian Hirsch, Nikolaj Nyvold Lundbye, Moritz Otto
In topological data analysis, the notions of persistent homology, birthtime, lifetime, and deathtime are used to assign and capture relevant cycles (i.e., topological features) of…