Ginibre系综特征多项式的最大值
概率论
2020-08-26 v3
摘要
当随机矩阵的维数趋于无穷时，我们计算了Ginibre系综的（中心化）特征多项式绝对值对数的最大值的主渐近性。该方法依赖于场的对数相关结构，我们通过构造与在小中尺度上某种正则化相关联的一族高斯乘性混沌测度，得到了最大值的下界。我们还得到了厚点集维数的主渐近性，并验证其与高斯自由场的预测一致。一个关键的技术输入是Ameur-Hedenmalm-Makarov推导必要渐近性的方法，以及Webb-Wong的结果。
引用
@article{arxiv.1902.01983,
title = {Maximum of the characteristic polynomial of the Ginibre ensemble},
author = {Gaultier Lambert},
journal= {arXiv preprint arXiv:1902.01983},
year = {2020}
}
备注
Typos corrected and some proofs have been clarified thanks to the referee's comments. 3 figures and references added. The appendix on the second moment of the characteristic polynomial have been removed since this result is already in the work of Akemann-Vernizzi [1]. Version accepted for publication in Comm. Math. Phys