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math.PR2024
The structure of entrance and exit at infinity for time-changed Lévy processes
Samuel Baguley, Leif Döring, Quan Shi
Studying the behaviour of Markov processes at boundary points of the state space has a long history, dating back all the way to William Feller. With different motivations in mind e…
cs.DS2024
Hyperbolic Random Graphs: Clique Number and Degeneracy with Implications for Colouring
Samuel Baguley, Yannic Maus, Janosch Ruff +1
Hyperbolic random graphs inherit many properties that are present in real-world networks. The hyperbolic geometry imposes a scale-free network with a strong clustering coefficient.…
math.PR2024
Uniqueness of locally stable Gibbs point processes via spatial birth-death dynamics
Samuel Baguley, Andreas Göbel, Marcus Pappik
We prove that for every locally stable and tempered pair potential with bounded range, there exists a unique infinite-volume Gibbs point process on for every act…