Numerical Study of Gap Distributions in Determinantal Point Process on Low Dimensional Spheres: L-Ensemble of O(n) Model Type for n = 2 and n = 3
Master of Arts (M.A.)
Degree Granting Department
Mathematics and Statistics
Seung-Yeop Lee, Ph.D.
Lu Lu, Ph.D.
Kandethody Ramachandran, Ph.D.
Circular Unitary Ensemble, Ginibre Ensemble, Hypothesis Test, Poisson Point Process
Poisson point process is the most well-known point process with many applications. Unlike Poisson point process, which is the random set of non-intersecting points, determinantal point process refers to certain class of point processes where the points tend to interact with each other. The interaction often leads to more uniformly distributed points compared to those in Poisson point process.
In this article, we study the gap distribution of certain class of determinantal point process, L-ensemble of O(n) model type, and compare the distribution with the ones from the other known determinantal point process that appears in random matrices. Our numerical results suggest that our determinantal point process model converges to the known random matrices, hinting at the universality in the statistical limit.
Scholar Commons Citation
Yang, Xiankui, "Numerical Study of Gap Distributions in Determinantal Point Process on Low Dimensional Spheres: L-Ensemble of O(n) Model Type for n = 2 and n = 3" (2020). USF Tampa Graduate Theses and Dissertations.