Large deviations principle for biorthogonal ensembles and variational formulation for the Dykema-Haagerup distribution

与杨图相关的随机矩阵

Random matrices associated to Young diagrams

该研究分析杨图形状分块随机矩阵的奇异值分布，证明其平方经验分布收敛于矩为推广卡特兰数的极限分布，给出超几何表示，并在特例中复现经典测度，还得到矩的复变量因式分解推广。

Random matrices, continuous circular systems and the triangular operator

We present a Hilbert space approach to the limit joint *-distributions of complex independent Gaussian random matrices. For that purpose, we use a suitably defined family of creation and annihilation operators living in some direct integral of Hilbert spaces. These operators are decomposed in terms of continuous circular systems of operators acting between the fibers of the considered Hilbert space direct integral. In the case of square matrices with i.i.d. entries, we obtain the circular operators of Voiculescu, whereas in the case of upper-triangular matrices with i.i.d. entries, we obtain t…