| Title | Beurling-Landau densities of weighted Fekete sets and correlation kernel estimates |
| Authors | Yacin Ameur, Joaquim Ortega-Cerda |
| Alternative Location | http://dx.doi.org/10.1016/j..., Restricted Access |
| Publication | Journal of Functional Analysis |
| Year | 2012 |
| Volume | 263 |
| Issue | 7 |
| Pages | 1825 - 1861 |
| Document type | Article |
| Status | Published |
| Quality controlled | Yes |
| Language | eng |
| Publisher | Elsevier |
| Abstract English | Let Q be a suitable real function on C. An n-Fekete set corresponding to Q is a subset {z(n vertical bar) , . . . , z(nn)} of C which maximizes the expression Pi(n)(i<j) vertical bar z(ni) - z(nj)vertical bar(2)e(-n(Q(zn1)) + . . . +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(zn vertical bar) + . . . + delta(znn)) converges to the equilibrium measure Delta Q . 1(s) dA as n -> infinity. 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 = vertical bar z vertical bar(2) we obtain results which hold globally, and we conjecture that such global results are true for a wide range of potentials. (C) 2012 Elsevier Inc. All rights reserved. |
| Keywords | Weighted Fekete set, Droplet, Equidistribution, Concentration operator, Correlation kernel, |
| ISBN/ISSN/Other | ISSN: 0022-1236 |
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