论文标题
Laplacian随机矩阵的极端特征值带有高斯条目
Extreme eigenvalues of Laplacian random matrices with Gaussian entries
论文作者
论文摘要
拉普拉斯矩阵是一个真实的对称矩阵，其行和列总和为零。我们研究了带有高斯条目的拉普拉斯随机矩阵的最大特征值的限制分布。与许多经典矩阵合奏不同，此随机矩阵模型包含相关条目。我们的主要结果表明，该模型的极端特征值显示了泊松统计。特别是，在正确转移和缩放后，我们表明，随着矩阵的尺寸倾向于无穷大，最大的特征值会收敛到牙龈分布。虽然最大的对角线进入也显示出牙龈波动，但其确定性居中项与最大特征值所需的中心项之间存在相当令人惊讶的差异。
A Laplacian matrix is a real symmetric matrix whose row and column sums are zero. We investigate the limiting distribution of the largest eigenvalues of a Laplacian random matrix with Gaussian entries. Unlike many classical matrix ensembles, this random matrix model contains dependent entries. Our main results show that the extreme eigenvalues of this model exhibit Poisson statistics. In particular, after properly shifting and scaling, we show that the largest eigenvalue converges to the Gumbel distribution as the dimension of the matrix tends to infinity. While the largest diagonal entry is also shown to have Gumbel fluctuations, there is a rather surprising difference between its deterministic centering term and the centering term required for the largest eigenvalues.
