论文标题
在随机单位矩阵的特征多项式的关节矩
On the joint moments of the characteristic polynomials of random unitary matrices
论文作者
论文摘要
我们建立了一个随机单位矩阵的特征多项式的联合力矩的渐近学及其对指数的一般实际价值的衍生物的衍生物，这证明了休斯在2001年做出的猜想。此外，我们为实际变化的型号而言，为领先的阶段而言，我们给出了一个概率的代表，该作用是在不合时宜的角色上，即涉及重要的角色。 Hua-Pickrell措施。这使我们能够在此随机变量的特征函数与$σ$-PainlevéIII'方程之间建立连接。
We establish the asymptotics of the joint moments of the characteristic polynomial of a random unitary matrix and its derivative for general real values of the exponents, proving a conjecture made by Hughes in 2001. Moreover, we give a probabilistic representation for the leading order coefficient in the asymptotic in terms of a real-valued random variable that plays an important role in the ergodic decomposition of the Hua-Pickrell measures. This enables us to establish connections between the characteristic function of this random variable and the $σ$-Painlevé III' equation.
