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arXiv · 1110.0284

Beurling-Landau densities of weighted Fekete sets and correlation kernel estimates

Yacin Ameur·Joaquim Ortega-Cerdà
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Abstract

In this paper we discuss equidistribution results for weighted Fekete sets in subsets of the plane. More precisely, we show that Fekete sets are maximally spread out relative to a rescaled version of the Beurling--Landau density, in the "droplet" corresponding to the given weight. Our method combines Landau's idea to relate the density of a family of discrete sets to properties of the spectrum of the concentration operator, with estimates for the correlation kernel of the corresponding random normal matrix ensemble.

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Yacin Ameur, Joaquim Ortega-Cerdà. 2011-10-03. Beurling-Landau densities of weighted Fekete sets and correlation kernel estimates. https://doi.org/10.1016/j.jfa.2012.06.011

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