Material Science and Thermodynamics Open access Peer reviewed

Orthogonal Polynomials in the Spherical Ensemble with Two Insertions

Sung‐Soo Byun, Peter J. Forrester, Arno B. J. Kuijlaars, Sampad Lahiry

SIAM Journal on Mathematical Analysis | Jul 14, 2026

Abstract

Abstract. We consider asymptotics of planar orthogonal polynomials [Formula: see text] (where [Formula: see text]) with respect to the weight [Formula: see text] in the whole complex plane. With [Formula: see text] and [Formula: see text] fixed, we obtain the strong asymptotics of the polynomials, asymptotics for the weighted [Formula: see text] norm, and the limiting zero counting measure. These results apply to the pre-critical phase of the underlying two-dimensional Coulomb gas system, when the support of the equilibrium measure is simply connected. Our method relies on specifying the mother body of the two-dimensional potential problem. It relies too on the fact that the planar orthogonality can be rewritten as a non-Hermitian contour orthogonality. This allows us to perform the Deift–Zhou steepest descent analysis of the associated [Formula: see text] Riemann–Hilbert problem.

Direct answer

What can I do from this paper page?

Use this page to scan "Orthogonal Polynomials in the Spherical Ensemble with Two Insertions" quickly: start with the summary and abstract, then check the authors, source, topics, and related papers. From here, open Scollr to follow Material Science and Thermodynamics research, save the paper, or map adjacent work.

Authors

Researchers on this paper

Sung‐Soo Byun

first | Seoul National University | ORCID 0000-0002-2405-2089

Peter J. Forrester

middle | The University of Melbourne | ORCID 0000-0002-9328-1387

Arno B. J. Kuijlaars

middle | KU Leuven | ORCID 0000-0001-6835-0945

Sampad Lahiry

last | The University of Melbourne

Research areas

Follow related topics

Mathematical functions and polynomials Material Science and Thermodynamics Latest Electromagnetic Scattering and Analysis research

Citation

BibTeX

@article{Byun2026Orthogonal,
  title = {Orthogonal Polynomials in the Spherical Ensemble with Two Insertions},
  author = {Sung‐Soo Byun and Peter J. Forrester and Arno B. J. Kuijlaars and Sampad Lahiry},
  journal = {SIAM Journal on Mathematical Analysis},
  year = {2026},
  doi = {10.1137/25m1764025},
  url = {https://doi.org/10.1137/25m1764025}
}

FAQ

Using this paper in a discovery workflow

How do I find related work for this paper?

Use the related papers and topic links on this page as starting points. In Scollr, you can also open the paper and build a literature map around its references, citing papers, and related work.

How can I keep up with new Material Science and Thermodynamics research papers?

Follow Material Science and Thermodynamics research in Scollr. New papers from the topic flow into a personalized feed, and you can save useful studies to revisit later.

Can I cite this paper from this page?

This page includes a static BibTeX block for Orthogonal Polynomials in the Spherical Ensemble with Two Insertions. Always verify the DOI, source, and publication details against the publisher record before submitting a manuscript.

Follow this research in Scollr

Follow the topics and authors behind this paper, save useful studies, and build a literature map when you are ready to go deeper.

Get the app