Griendt, Jesher van der (2024) Coupling of functionals of Determinantal point processes and Poisson point processes. Bachelor's Thesis, Mathematics.
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Abstract
We prove a Poisson process approximation result for stabilizing functionals of a determinantal point process. Our results use concrete couplings of determinantal processes with different Palm measures and exploit their association properties. Second, we focus on the Ginibre process and show in the asymptotic scenario of an increasing observation window that the process of points with a large nearest neighbor distance converges after a suitable scaling to a Poisson point process. As a corollary, we obtain the scaling of the maximum nearest neighbor distance in the Ginibre process, which turns out to be different from its analogue for independent points.
| Item Type: | Thesis (Bachelor's Thesis) |
|---|---|
| Supervisor name: | Bonnet, G.F.Y. and Szabo, R. |
| Degree programme: | Mathematics |
| Thesis type: | Bachelor's Thesis |
| Language: | English |
| Date Deposited: | 15 Jul 2024 08:41 |
| Last Modified: | 15 Jul 2024 08:41 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/33343 |
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