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Title: Beurling-Landau densities of weighted Fekete sets and correlation kernel estimates
Author: Ameur, Yacin
Ortega Cerdà, Joaquim
Keywords: Teoria del potencial (Matemàtica)
Potential theory (Mathematics)
Issue Date: 1-Oct-2012
Publisher: Elsevier
Abstract: Let $Q$ be a suitable real function on $C$. An $n$-Fekete set corresponding to $Q$ is a subset ${Z_{n1}},\dotsb, Z_{nn}}$ of $C$ which maximizes the expression $\Pi^n_i_{<j}|Z_{ni} - Z_{nj}|^2 e^-^{n(Q(Z_n_1)+\dotsb+Q(Z_{nn}))}$. It is well known that, under reasonable conditions on $Q$, there is a compact set $S$ known as the 'droplet' such that the measures $\mu_n n^{-1} (\delta_{zn1}+\dots+\delta_{znn})$ converges to the equilibrium measure $\Delta Q.1 _S$d$A$ as $n \rightarrow \infty$. In this note we prove that Fekete sets are, in a sense, maximally spread out with respect to the equilibrium measure. In general, our results apply only to a part of the Fekete set, which is at a certain distance away from the boundary of the droplet. However, for the potential $Q=|Z|^2$ we obtain results which hold globally, and we conjecture that such global results are true for a wide range of potentials.
Note: Versió postprint del document publicat a:
It is part of: Journal of Functional Analysis, 2012, vol. 263, num. 7, p. 1825-1861
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ISSN: 0022-1236
Appears in Collections:Articles publicats en revistes (Matemàtiques i Informàtica)

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