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arXiv · 1804.08587

The random normal matrix model: insertion of a point charge

Yacin Ameur·Nam-Gyu Kang·Seong-Mi Seo
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Abstract

In this article, we study microscopic properties of a two-dimensional eigenvalue ensemble near a conical singularity arising from insertion of a point charge in the bulk of the support of eigenvalues. In particular, we characterize all rotationally symmetric scaling limits ('Mittag-Leffler fields') and obtain universality of them when the underlying potential is algebraic. Applications include a result on the asymptotic distribution of $\log|p_n(ζ)|$ where $p_n$ is the characteristic polynomial of an $n$:th order random normal matrix.

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Yacin Ameur, Nam-Gyu Kang, Seong-Mi Seo. 2021-08-06. The random normal matrix model: insertion of a point charge. https://doi.org/10.1007/s11118-021-09942-z

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