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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 |
URI: | http://hdl.handle.net/2445/102303 |
Related resource: | http://dx.doi.org/10.1016/j.jco.2016.08.001 |
ISSN: | 0885-064X |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
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