Abstract
We study random normal matrix models whose eigenvalues tend to be distributed within a narrow “band” around the unit circle of width proportional to , where n is the size of matrices. For general radially symmetric potentials with various boundary conditions, we derive the scaling limits of the correlation functions, some of which appear in the previous literature notably in the context of almost-Hermitian random matrices. We also obtain that fluctuations of the maximal and minimal modulus of the ensembles follow the Gumbel or exponential law depending on the boundary conditions.
Funding Statement
Sung-Soo Byun was supported by Samsung Science and Technology Foundation (SSTF-BA1401-51), by the National Research Foundation of Korea (NRF-2019R1A5A1028324) and by a KIAS Individual Grant (SP083201) via the Center for Mathematical Challenges at Korea Institute for Advanced Study. Seong-Mi Seo was partially supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2019R1A5A1028324 and No. 2019R1F1A1058006).
Acknowledgements
It is our pleasure to thank Yacin Ameur for helpful discussions.
Citation
Sung-Soo Byun. Seong-Mi Seo. "Random normal matrices in the almost-circular regime." Bernoulli 29 (2) 1615 - 1637, May 2023. https://doi.org/10.3150/22-BEJ1514
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