标题： 自由卷积的相互作用粒子系统解释 显示英文标题

标题： An Interacting Particle System Interpretation of Free Convolution

摘要： 大型随机矩阵之和的特征值谱，当这些矩阵相互“自由”，即随机旋转时，可以使用R变换的形式来获得，在不同领域有许多应用。我们提供了一种直接解释，将R变换的抽象可加性性质用于和的情况，以一种确定性的动力学演化方式（粒子，即特征值）通过二体及更高体作用力相互作用，推广了通常的库仑相互作用。我们将结果扩展到自由矩阵的乘积。 显示英文摘要

摘要： The eigenvalue spectrum of the sum of large random matrices that are mutually "free", i.e. randomly rotated, can be obtained using the formalism of R-transforms, with many applications in different fields. We provide a direct interpretation of the otherwise abstract additivity property of R-transforms for the sum in terms of a deterministic dynamical evolution of "particles" (the eigenvalues), interacting through two-body and higher-body forces, generalizing the usual Coulomb interaction. We extend our result to product of free matrices.