PreprintarXiv licencearXiv
Precise universal edge asymptotics for planar β=2 Coulomb gases with radial external fields
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 (25loglog n)/(4elog n) and (2loglog n)/(elog 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.
Related
- Influence Diagnostics in High-dimensional M-estimation: Precise Asymptotics
- Precise Asymptotics for Dense High-Dimensional Huber Regression under Heteroscedasticity
- Phylogenetic Inference and the Stickiness of Fréchet Means, via Precise Asymptotics of an Embedded Random Walk
- Limit theorems for Coulomb gases on a Jordan curve in an external potential
- Precise spectral asymptotics, exponential localization, and spectral gap estimates for the three-boson lattice Schrödinger operator
BibTeX
@misc{ma2026precise,
title = {{Precise universal edge asymptotics for planar $β=2$ Coulomb gases with radial external fields}},
author = {Yutao Ma and Xujia Meng},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.27880},
eprint = {2608.27880},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.27880},
}
RIS
TY - UNPB
TI - Precise universal edge asymptotics for planar β=2 Coulomb gases with radial external fields
AU - Yutao Ma
AU - Xujia Meng
PY - 2026
DA - 2026/08/28
PB - arXiv
DO - 10.48550/arxiv.2608.27880
UR - https://arxiv.org/abs/2608.27880
AB - 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 (25loglog n)/(4elog n) and (2loglog n)/(elog 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.
ER -