AI 中文总结
该研究针对带径向外场的平面β=2库仑气体，建立了最右侧特征值与谱半径收敛到Gumbel分布的精确Berry–Esseen界，推导了其大、中偏差的精确渐近等价关系，最小模也有类似结果。
AI 中文摘要
我们研究带径向外场的平面β=2库仑气体的极值统计特性。针对最右侧特征值与谱半径，我们建立了它们收敛到Gumbel分布的精确Berry–Esseen界，对应显式速率分别为(25loglog n)/(4e log n)和(2loglog n)/(e log n)；此外，我们推导了这两类统计量在所有相关尺度下的大偏差与中偏差的精确渐近等价关系，最小模也存在类似结果。
英文摘要
We investigate the extremal statistics of planar $β=2$ 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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