Precise universal edge asymptotics for planar $β=2$ Coulomb gases with radial external fields
Year: 2026
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Ma, Yutao, Meng, Xujia
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G7611008738
OpenAlex ID: W7204843385