论文标题
beta jacobi合奏和相关的雅各比多项式
Beta Jacobi ensembles and associated Jacobi polynomials
论文作者
论文摘要
现在，具有三个经典权重（高斯，拉瓜尔和雅各比）在真实线上的beta合奏现在已被实现为某些三角形随机矩阵的特征值。该论文涉及Beta Jacobi合奏，这种类型具有Jacobi重量。利用随机矩阵模型，我们表明，在[0，\ infty）$中的$βn\ to const \ $ n $中，系统大小的经验分布微弱地收敛于限制性措施，该措施属于属于雅各比jacobi jacobi polynomials的新概率测量。这类似于其他两个经典权重的现有结果。我们还研究了同一制度中β雅各比过程的经验测量过程的限制行为，并获得了上述动态版本。
Beta ensembles on the real line with three classical weights (Gaussian, Laguerre and Jacobi) are now realized as the eigenvalues of certain tridiagonal random matrices. The paper deals with beta Jacobi ensembles, the type with the Jacobi weight. Making use of the random matrix model, we show that in the regime where $βN \to const \in [0, \infty)$, with $N$ the system size, the empirical distribution of the eigenvalues converges weakly to a limiting measure which belongs to a new class of probability measures of associated Jacobi polynomials. This is analogous to the existing results for the other two classical weights. We also study the limiting behavior of the empirical measure process of beta Jacobi processes in the same regime and obtain a dynamic version of the above.
