1 citations · 1 across the 6 of their papers we have counts for
7 papers
Large deviations for sparse systems of moving particles
Cairui Duan, Paula de Dios Andres, Manish Pandey +3
We study large deviations for rare clusters in sparse systems of moving particles. In the regime \(nr_n^d\to0\) and \(ρ_{k,n}=n^kr_n^{d(k-1)}\to\infty\), we prove a large deviation…
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…
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…
Limit theorems under heavy-tailed scenario in the age dependent random connection models
Christian Hirsch, Takashi Owada
This paper considers limit theorems associated with subgraph counts in the age-dependent random connection model. First, we identify regimes where the count of sub-trees converges…
Cumulant method for weighted random connection models
Nils Heerten, Christian Hirsch, Moritz Otto
In this paper, we derive cumulant bounds for subgraph counts and power-weighted edge length in a class of spatial random networks known as weighted random connection models. This i…
Normal approximation for Gibbs processes via disagreement couplings
Christian Hirsch, Moritz Otto, Anne Marie Svane
This work improves the existing central limit theorems (CLTs) for geometric functionals of Gibbs processes in three aspects. First, we derive a CLT for weakly stabilizing functiona…