Ameur, YacinOrtega Cerdà, Joaquim2013-04-222013-04-222012-10-010022-1236https://hdl.handle.net/2445/34752Let $Q$ 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.37 p.application/pdfeng(c) Elsevier, 2012Teoria del potencial (Matemàtica)Potential theory (Mathematics)info:eu-repo/semantics/article6154252013-04-22info:eu-repo/semantics/openAccess