Abstract
In this article, we study microscopic properties of a two-dimensional Coulomb gas ensemble near a conical singularity arising from insertion of a point charge in the bulk of the droplet. In the determinantal case, we characterize all rotationally symmetric scaling limits (“Mittag-Leffler fields”) and obtain universality of them when the underlying potential is algebraic. Applications include a central limit theorem for \(\log |p_{n}(\zeta )|\) where pn is the characteristic polynomial of an n:th order random normal matrix.
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Nam-Gyu Kang was partially supported by Samsung Science and Technology Foundation (SSTF-BA1401-51), a KIAS Individual Grant (MG058103) at Korea Institute for Advanced Study, and National Research Foundation of Korea under grant number NRF-2019R1A5A1028324.
Seong-Mi Seo was partially supported by a KIAS Individual Grant (MG063103) at Korea Institute for Advanced Study and by the National Research Foundation of Korea, grant number 2019R1F1A1058006 and NRF-2019R1A5A1028324.
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Ameur, Y., Kang, NG. & Seo, SM. The Random Normal Matrix Model: Insertion of a Point Charge. Potential Anal 58, 331–372 (2023). https://doi.org/10.1007/s11118-021-09942-z
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DOI: https://doi.org/10.1007/s11118-021-09942-z