可积随机矩阵系综
Integrable random matrix ensembles
摘要：
我们提出了一类新的随机矩阵合奏的统计性质是中间的统计Wigner-Dyson随机矩阵和泊松统计。该结构是基于可积N体经典系统的动量和坐标的粒子的随机分布。这些系统的Lax矩阵产生随机矩阵集合，其特征值的联合分布可以通过分析计算，这要归功于底层系统的可积性。间距分布和水平可压缩性的公式，得到了各种情况下，这样的合奏。
英文摘要：
We propose new classes of random matrix ensembles whose statistical properties are intermediate between statistics of Wigner-Dyson random matrices and Poisson statistics. The construction is based on integrable N-body classical systems with a random distribution of momenta and coordinates of the particles. The Lax matrices of these systems yield random matrix ensembles whose joint distribution of eigenvalues can be calculated analytically thanks to integrability of the underlying system. Formulas for spacing distributions and level compressibility are obtained for various instances of such ensembles.
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