Electrostatic fields due to distributions of electrons (Q1355475)

Let \(K\) be a compact set of positive capacity in \(\mathbb{R}^n\), \(n\geq 2\), and let \(\omega\) be the equilibrium distribution for \(K\). Choose \(N\) points of \(K\) and let \(\mu_N\) denote the probability measure corresponding to the point charges \({1\over N}\) at these points; if the potential energy due to these discrete measures is minimal, the corresponding mass distribution defines a Fekete equilibrium distribution \(\omega_N\). This interesting survey article (including some nice new results) discusses the approximation of \(\mu_N\) to \(\omega\) by considering the differences \(\omega(E)- \mu_N(E)\) for some regular sets \(E\), the potentials \(U^{\mu_n}\) and \(U^\omega\), and the electrostatic fields \(\varepsilon^\omega\) and \(\varepsilon^{\mu_N}\).