We study moments of characteristic polynomials of truncated Haar distributed matrices from the three classical compact groups $\mathrm{\text{O(N)}}$, $\mathrm{\text{U(N)}}$ and $\mathrm{\text{Sp(2N)}}$. For finite matrix size we calculate the moments in terms of hypergeometric functions of matrix argument and give explicit integral representations highlighting the duality between the moment and the matrix size as well as the duality between the orthogonal and symplectic cases. Asymptotic expansions in strong and weak non-unitarity regimes are obtained. Using the connection to matrix hypergeometric functions, we establish limit theorems for the log-modulus of the characteristic polynomial evaluated on the unit circle.

中文翻译：

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随机截断的特征多项式：矩、对偶和渐近

我们研究了来自三个经典紧群的截断 Haar 分布矩阵的特征多项式的矩$\mathrm{\text{在）}}$,$\mathrm{\text{联合国）}}$和$\mathrm{\text{Sp(2N)}}$. 对于有限矩阵大小，我们根据矩阵参数的超几何函数计算矩，并给出显式积分表示，突出矩和矩阵大小之间的对偶性以及正交和辛情况之间的对偶性。获得了强和弱非酉体系的渐近展开。利用与矩阵超几何函数的联系，我们建立了单位圆上特征多项式的对数模的极限定理。