复 Ginibre 系综圆律的收敛速率
概率论
2015-07-22 v3 数学物理
math.MP
摘要
我们证明了复 Ginibre 系综圆律的收敛速率。具体而言，我们界定了归一化复 Ginibre 系综的经验谱测度与单位圆盘上的均匀测度之间期望 -Wasserstein 距离的上下界，包括在期望意义下和几乎必然意义下。对于 ，该界为 量级（至多相差对数因子）。
引用
@article{arxiv.1406.1396,
title = {A rate of convergence for the circular law for the complex Ginibre ensemble},
author = {Elizabeth S. Meckes and Mark W. Meckes},
journal= {arXiv preprint arXiv:1406.1396},
year = {2015}
}
备注
Final version: to appear in Annales de la Facult\'e des Sciences de Toulouse. Previous comments: New result added giving almost sure convergence rates in addition to rates in expectation. One figure added to illustrate an initial segment with respect to the spiral order. Several references to related work added