高斯四元数矩阵的随机右特征值
Random right eigenvalues of Gaussian quaternionic matrices
摘要：
我们考虑一个随机矩阵，其元素是独立的高斯变量，其值在四元数域中，方差为$1/n$。利用对数位势论，证明了当维数$n$趋于无穷大时，四元数场右本征值的经验分布对单位球上的某个测度的几乎必然收敛性.对更一般的高斯四元数随机矩阵模型也作了一些评论。
英文摘要：
We consider a random matrix whose entries are independent Gaussian variables taking values in the field of quaternions with variance $1/n$. Using logarithmic potential theory, we prove the almost sure convergence, as the dimension $n$ goes to infinity, of the empirical distribution of the right eigenvalues towards some measure supported on the unit ball of the quaternions field. Some comments on more general Gaussian quaternionic random matrix models are also made.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
