论文标题
随机正交和符号矩阵的特征多项式矩
Moments of Moments of the Characteristic Polynomials of Random Orthogonal and Symplectic Matrices
论文作者
论文摘要
使用Toeplitz+Hankel决定因素的渐近学，我们为随机正交和符号矩阵的特征多项式时刻的矩矩创建了公式，因为基质大小倾向于无限。我们的结果类似于[14]中FAHS获得随机单位矩阵的结果。我们得出的公式的一个关键特征是，在矩的矩中，相变的相变依赖于所讨论的对称组。
Using asymptotics of Toeplitz+Hankel determinants, we establish formulae for the asymptotics of the moments of the moments of the characteristic polynomials of random orthogonal and symplectic matrices, as the matrix-size tends to infinity. Our results are analogous to those that Fahs obtained for random unitary matrices in [14]. A key feature of the formulae we derive is that the phase transitions in the moments of moments are seen to depend on the symmetry group in question in a significant way.
