标题： 有限自由点过程 显示英文标题

标题： Finite Free Point Processes

摘要： 我们使用有限自由概率的技术来分析与随机矩阵的特征值、奇异值和广义奇异值相关的矩阵过程。 我们使用的模型非常基础，分析完全由期望特征多项式组成。 我们的若干结果与随机矩阵理论中的已知结果相匹配，然而我们的主要结果（关于广义奇异值）似乎比该领域中的标准随机矩阵过程（Hermite/Laguerre/Jacobi）更为一般。 为了验证这一点，我们对该新过程进行了一系列模拟，一方面确认该过程可以表现出在标准随机矩阵过程中未见过的行为，另一方面提供了证据表明我们的技术能够很好地捕捉真实行为。 结合我们能够为此新模型计算出与标准模型相同的统计量这一事实，这表明进一步的研究可能既有趣又有成效。 显示英文摘要

摘要： We use techniques from finite free probability to analyze matrix processes related to eigenvalues, singular values, and generalized singular values of random matrices. The models we use are quite basic and the analysis consists entirely of expected characteristic polynomials. A number of our results match known results in random matrix theory, however our main result (regarding generalized singular values) seems to be more general than any of the standard random matrix processes (Hermite/Laguerre/Jacobi) in the field. To test this, we perform a series of simulations of this new process that, on the one hand, confirms that this process can exhibit behavior not seen in the standard random matrix processes, but on the other hand provides evidence that the true behavior is captured quite well by our techniques. This, coupled with the fact that we are able to compute the same statistics for this new model that we are for the standard models, suggests that further investigation could be both interesting and fruitful.