Szeg\H{o} type correlations for two-dimensional outpost ensembles

TL;DR

This paper investigates universal correlation asymptotics in two-dimensional Coulomb systems with outposts, extending Szegő-type edge correlation results and analyzing effects of external charges.

Contribution

It generalizes Szegő-type edge correlations to systems with outposts and explores the impact of external point charges within this framework.

Findings

Correlation asymptotics are universal and expressed via a reproducing kernel.

Generalization of Szegő-type edge correlations to outpost systems.

Insertion of exterior point charges affects correlation structures.

Abstract

We consider two-dimensional Coulomb systems for which the coincidence set contains an outpost in the form of a suitable Jordan curve. We study asymptotics for correlations along the union of the outpost and the outer boundary of the droplet. These correlations turn out to have a universal character and are given in terms of the reproducing kernel for a certain Hilbert space of analytic functions, generalizing the Szeg\H{o} type edge correlations obtained recently by Ameur and Cronvall. There are several additional results, for example on the effect of insertion of an exterior point charge in the presence of an outpost.