标题： 行列式相关性对于经典投影过程 显示英文标题

标题： Determinantal Correlations for Classical Projection Processes

摘要： 最近在排队论和统计力学中的应用已经确定了由GUE特征值的连续子式形成的过程。 一般而言，从经典随机矩阵系综的随机秩1投影产生的嵌套矩阵序列的特征值形成的类似特征值过程，在LUE和JUE中被识别出来。 所有这些过程的相关性都可以以统一的方式计算。 然后可以对所得表达式进行各种尺度极限分析。 在软边缘处，当子式的秩相差一个与$N^{2/3}$成比例的量时，缩放后的相关性与从Dyson布朗运动模型的软边缘尺度已知的相关性一致。 显示英文摘要

摘要： Recent applications in queuing theory and statistical mechanics have isolated the process formed by the eigenvalues of successive minors of the GUE. Analogous eigenvalue processes, formed in general from the eigenvalues of nested sequences of matrices resulting from random corank 1 projections of classical random matrix ensembles, are identified for the LUE and JUE. The correlations for all these processes can be computed in a unified way. The resulting expressions can then be analyzed in various scaling limits. At the soft edge, with the rank of the minors differing by an amount proportional to $N^{2/3}$, the scaled correlations coincide with those known from the soft edge scaling of the Dyson Brownian motion model.