Scaling limit for determinantal point processes on spheres

Makoto Katori, Tomoyuki Shirai

Research output: Contribution to journalArticlepeer-review

Abstract

The unitary group with the Haar probability measure is called Circular Unitary Ensemble. All the eigenvalues lie on the unit circle in the complex plane and they can be regarded as a determinantal point process on S1. It is also known that the scaled point processes converge weakly to the determinantal point process associated with the so-called sine kernel as the size of matrices tends to ∞. We extend this result to the case of high-dimensional spheres and show that the scaling limit processes are determinantal point processes associated with the kernels expressed by the Bessel functions of the first kind
Original languageEnglish
Pages (from-to)123-138
JournalRIMS Kokyuroku Bessatsu
VolumeB79
Publication statusPublished - Apr 2020

Fingerprint

Dive into the research topics of 'Scaling limit for determinantal point processes on spheres'. Together they form a unique fingerprint.

Cite this