Beurling–Landau densities of weighted Fekete sets and correlation kernel estimates
- Ameur, Yacin
- Ortega-Cerdà, Joaquim
DOIAbstract
AbstractLet Q be a suitable real function on C. An n-Fekete set corresponding to Q is a subset {zn1,…,znn} of C which maximizes the expression ∏i<jn|zni−znj|2e−n(Q(zn1)+⋯+Q(znn)). It is well known that, under reasonable conditions on Q, there is a compact set S known as the “droplet” such that the measures μn=n−1(δzn1+⋯+δznn) converges to the equilibrium measure ΔQ⋅1SdA as n→∞. 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 a...