Open Access
December 2022 Local universality of determinantal point processes on Riemannian manifolds
Makoto Katori, Tomoyuki Shirai
Proc. Japan Acad. Ser. A Math. Sci. 98(10): 95-100 (December 2022). DOI: 10.3792/pjaa.98.018

Abstract

We consider the Laplace-Beltrami operator $\Delta_{g}$ on a smooth, compact Riemannian manifold $(M,g)$ and the determinantal point process $\mathcal{X}_{\lambda}$ on $M$ associated with the spectral projection of $-\Delta_{g}$ onto the subspace corresponding to the eigenvalues up to $\lambda^{2}$. We show that the pull-back of $\mathcal{X}_{\lambda}$ by the exponential map $\exp_{p} : T_{p}^{*}M \to M$ under a suitable scaling converges weakly to the universal determinantal point process on $T_{p}^{*} M$ as $\lambda \to \infty$.

Citation

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Makoto Katori. Tomoyuki Shirai. "Local universality of determinantal point processes on Riemannian manifolds." Proc. Japan Acad. Ser. A Math. Sci. 98 (10) 95 - 100, December 2022. https://doi.org/10.3792/pjaa.98.018

Information

Published: December 2022
First available in Project Euclid: 30 November 2022

zbMATH: 1508.60055
Digital Object Identifier: 10.3792/pjaa.98.018

Subjects:
Primary: 46E22 , 60G55
Secondary: 60B20

Keywords: Bessel functions , Determinantal point process on Riemannian manifolds , Euclidean motion group , local universality , pointwise Weyl law , spectral projection

Rights: Copyright © 2022 The Japan Academy

Vol.98 • No. 10 • December 2022
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