真实Ginibre系综的极值律
Extremal laws for the real Ginibre ensemble
摘要：
真正的Ginibre系综是指家庭的$n\times n$矩阵，其中每个条目是一个独立的高斯随机变量的均值为零，方差为1。我们的主要结果是，适当缩放的光谱半径收敛的法律Gumbel分布为$n\rightarrow\infty$。这一事实已经被称为持有在复杂的和四元数类似物的合奏了一段时间，与简单的证明。在此过程中，我们建立了一个新的形式的最大实特征值的极限定律。
英文摘要：
The real Ginibre ensemble refers to the family of $n\times n$ matrices in which each entry is an independent Gaussian random variable of mean zero and variance one. Our main result is that the appropriately scaled spectral radius converges in law to a Gumbel distribution as $n\rightarrow\infty$. This fact has been known to hold in the complex and quaternion analogues of the ensemble for some time, with simpler proofs. Along the way we establish a new form for the limit law of the largest real eigenvalue.
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