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http://hdl.handle.net/2445/34752
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: http://dx.doi.org/10.1016/j.jfa.2012.06.011 |
It is part of: | Journal of Functional Analysis, 2012, vol. 263, num. 7, p. 1825-1861 |
URI: | http://hdl.handle.net/2445/34752 |
Related resource: | http://dx.doi.org/10.1016/j.jfa.2012.06.011 |
ISSN: | 0022-1236 |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
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