Please use this identifier to cite or link to this item: http://hdl.handle.net/2445/102303
Title: Energy and discrepancy of rotationally invariant determinantal point processes in high dimensional spheres
Author: Beltrán, Carlos
Marzo Sánchez, Jordi
Ortega Cerdà, Joaquim
Keywords: Funcions hipergeomètriques
Teoria de nombres
Hypergeometric functions
Number theory
Issue Date: Dec-2016
Publisher: Elsevier
Abstract: We study expected Riesz s-energies and linear statistics of some determinantal processes on the sphere $\mathbb{S}^{d}$. In particular, we compute the expected Riesz and logarithmic energies of the determinantal processes given by the reproducing kernel of the space of spherical harmonics. This kernel defines the so called harmonic ensemble on $\mathbb{S}^{d}$. With these computations we improve previous estimates for the discrete minimal energy of configurations of points in the sphere. We prove a comparison result for Riesz 2-energies of points defined through determinantal point processes associated with isotropic kernels. As a corollary we get that the Riesz 2-energy of the harmonic ensemble is optimal among ensembles defined by isotropic kernels with the same trace. Finally, we study the variance of smooth and rough linear statistics for the harmonic ensemble and compare the results with the variance for the spherical ensemble (in $\mathbb{S}^{d}$).
Note: Versió postprint del document publicat a: http://dx.doi.org/10.1016/j.jco.2016.08.001
It is part of: Journal of Complexity, 2016, vol. 37, p. 76-109
Related resource: http://dx.doi.org/10.1016/j.jco.2016.08.001
URI: http://hdl.handle.net/2445/102303
ISSN: 0885-064X
Appears in Collections:Articles publicats en revistes (Matemàtiques i Informàtica)

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