Szeg\H{o} type correlations for two-dimensional outpost ensembles
Complex Variables
2026-03-09 v1 Mathematical Physics
math.MP
Probability
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.
Cite
@article{arxiv.2603.06191,
title = {Szeg\H{o} type correlations for two-dimensional outpost ensembles},
author = {Yacin Ameur and Ena Jahic},
journal= {arXiv preprint arXiv:2603.06191},
year = {2026}
}