Beurling-Landau densities of weighted Fekete sets and correlation kernel estimates
(2012) In Journal of Functional Analysis 263(7). p.1825-1861- Abstract
- 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... (More)
- 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. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/3146789
- author
- Ameur, Yacin LU and Ortega-Cerda, Joaquim
- organization
- publishing date
- 2012
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Weighted Fekete set, Droplet, Equidistribution, Concentration operator, Correlation kernel
- in
- Journal of Functional Analysis
- volume
- 263
- issue
- 7
- pages
- 1825 - 1861
- publisher
- Elsevier
- external identifiers
-
- wos:000307906800003
- scopus:84864839327
- ISSN
- 0022-1236
- DOI
- 10.1016/j.jfa.2012.06.01
- language
- English
- LU publication?
- yes
- id
- ab4efc7c-b8ba-4bfe-a4f9-973556b5489f (old id 3146789)
- date added to LUP
- 2016-04-01 14:17:51
- date last changed
- 2022-01-27 23:51:02
@article{ab4efc7c-b8ba-4bfe-a4f9-973556b5489f, abstract = {{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.}}, author = {{Ameur, Yacin and Ortega-Cerda, Joaquim}}, issn = {{0022-1236}}, keywords = {{Weighted Fekete set; Droplet; Equidistribution; Concentration operator; Correlation kernel}}, language = {{eng}}, number = {{7}}, pages = {{1825--1861}}, publisher = {{Elsevier}}, series = {{Journal of Functional Analysis}}, title = {{Beurling-Landau densities of weighted Fekete sets and correlation kernel estimates}}, url = {{http://dx.doi.org/10.1016/j.jfa.2012.06.01}}, doi = {{10.1016/j.jfa.2012.06.01}}, volume = {{263}}, year = {{2012}}, }