Precise universal edge asymptotics for planar $\beta=2$ Coulomb gases with radial external fields

Yutao Ma; Xujia Meng

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arXiv · 2608.27880

Precise universal edge asymptotics for planar $\beta=2$ Coulomb gases with radial external fields

Yutao Ma·Xujia Meng

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Abstract

We investigate the extremal statistics of planar $\beta=2$ Coulomb gases with radial external fields. For the rightmost eigenvalue and the spectral radius, we establish sharp Berry--Esseen bounds for their convergence to the Gumbel distribution, with explicit rates \[ \frac{25\log\log n}{4e\log n} \quad\text{and}\quad \frac{2\log\log n}{e\log n}, \] respectively. In addition, we derive sharp asymptotic equivalences for the large and moderate deviations of both statistics across all relevant scales. Analogous results hold for the smallest modulus.

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Yutao Ma, Xujia Meng. 2026-08-28. Precise universal edge asymptotics for planar $\beta=2$ Coulomb gases with radial external fields. https://arxiv.org/abs/2608.27880

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