论文标题
与古典正交合奏的平均值的渐近学
Asymptotics for averages over classical orthogonal ensembles
论文作者
论文摘要
我们研究正交HAAR分布式矩阵的集合中的乘法特征值统计的平均值，可以将其写入Toeplitz+Hankel的决定因素。在某些奇异性合并在一起的情况下，我们获得了具有Fisher-Hartwig奇点的符号的新渐近学，以及具有差距或差距的符号。我们通过依靠单位组中的已知类似结果和对单位圆上相关的正交多项式的渐近结果来获得这些渐近学。作为我们结果的结果，我们在圆形正交和符号合奏中得出了渐近概率的渐近概率，以及正交集合中全局特征值刚度的上限。
We study averages of multiplicative eigenvalue statistics in ensembles of orthogonal Haar distributed matrices, which can alternatively be written as Toeplitz+Hankel determinants. We obtain new asymptotics for symbols with Fisher-Hartwig singularities in cases where some of the singularities merge together, and for symbols with a gap or an emerging gap. We obtain these asymptotics by relying on known analogous results in the unitary group and on asymptotics for associated orthogonal polynomials on the unit circle. As consequences of our results, we derive asymptotics for gap probabilities in the Circular Orthogonal and Symplectic Ensembles, and an upper bound for the global eigenvalue rigidity in the orthogonal ensembles.
