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

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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• Critical exponents of the two dimensional Coulomb gas at the Berezinskii-Kosterlitz-Thouless transition
• Equidistribution of Fekete points on complex manifolds

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