BeurlingLandau densities of weighted Fekete sets and correlation kernel estimates
(2012) In Journal of Functional Analysis 263(7). p.18251861 Abstract
 Let Q be a suitable real function on C. An nFekete 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 nFekete 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:
http://lup.lub.lu.se/record/3146789
 author
 Ameur, Yacin ^{LU} and OrtegaCerda, 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
 00221236
 DOI
 10.1016/j.jfa.2012.06.01
 language
 English
 LU publication?
 yes
 id
 ab4efc7cb8ba4bfea4f9973556b5489f (old id 3146789)
 date added to LUP
 20121126 09:40:24
 date last changed
 20170702 04:05:32
@article{ab4efc7cb8ba4bfea4f9973556b5489f, abstract = {Let Q be a suitable real function on C. An nFekete 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 OrtegaCerda, Joaquim}, issn = {00221236}, keyword = {Weighted Fekete set,Droplet,Equidistribution,Concentration operator,Correlation kernel}, language = {eng}, number = {7}, pages = {18251861}, publisher = {Elsevier}, series = {Journal of Functional Analysis}, title = {BeurlingLandau densities of weighted Fekete sets and correlation kernel estimates}, url = {http://dx.doi.org/10.1016/j.jfa.2012.06.01}, volume = {263}, year = {2012}, }