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Edge Scaling Limit of the Spectral Radius for Random Normal Matrix Ensembles at Hard Edge

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Abstract

We investigate local statistics of eigenvalues for random normal matrices, represented as 2D determinantal Coulomb gases, in the case when the eigenvalues are forced to be in the support of the equilibrium measure associated with an external field. For radially symmetric external fields with sufficient growth at infinity, we show that the fluctuations of the spectral radius around a hard edge tend to follow an exponential distribution as the number of eigenvalues tends to infinity. As a corollary, we obtain the order statistics of the moduli of eigenvalues.

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Acknowledgements

The author thanks Nam-Gyu Kang for helpful advice and discussions. In addition, the author would like to thank the reviewers for several helpful comments on this manuscript. This work was partially supported by the KIAS Individual Grant (MG063103) at Korea Institute for Advanced Study and by the National Research Foundation of Korea Grant funded by the Korea government (2019R1F1A1058006).

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  1. School of Mathematics, Korea Institute for Advanced Study, 85 Hoegiro, Dongdaemun-gu, Seoul, 02455, Republic of Korea

    Seong-Mi Seo

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Correspondence to Seong-Mi Seo.

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Communicated by Abhishek Dhar.

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Seo, SM. Edge Scaling Limit of the Spectral Radius for Random Normal Matrix Ensembles at Hard Edge. J Stat Phys 181, 1473–1489 (2020). https://doi.org/10.1007/s10955-020-02634-9

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