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math.PR2024
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…
math.PR2024
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…