Asymptotic Approximate Fekete Arrays

TL;DR

This paper extends the concept of asymptotic Fekete arrays to a more flexible setting in weighted pluripotential theory, allowing points outside the compact set in higher dimensions, building on recent multidimensional work.

Contribution

It introduces a generalized definition of asymptotic Fekete arrays that permits points outside the set, expanding the applicability in weighted pluripotential theory for higher dimensions.

Findings

Generalized asymptotic Fekete arrays in higher dimensions.

Points in arrays can lie outside the compact set.

Relies on recent multidimensional pluripotential theory results.

Abstract

The notion of asymptotic Fekete arrays, arrays of points in a compact set $K\subset {\bf C}^d$ which behave asymptotically like Fekete arrays, has been well-studied, albeit much more recently in dimensions $d>1$. Here we show that one can allow a more flexible definition where the points in the array need not lie in $K$. Our results, which work in the general setting of weighted pluripotential theory, rely heavily, in the multidimensional setting, on the ground-breaking work of Berman, Boucksom and Nystrom.