论文标题
WishArt过程：平均场限制，长时间行为和自由概率
Wishart processes : mean-field limit, long time behavior, and free probability
论文作者
论文摘要
本文致力于研究Wishart过程的特征值，该过程类似于Dyson Brownian Motion用于协方差矩阵。此类过程特别研究了Bybru。这些特征值的经验度量的平均场融合被证明是Malecki andPerez。在本文中，我们使用Benaych-Georges开发的自由矩形卷积理论的工具为平均场收敛问题提供了一种新的方法，该理论尤其允许允许明确计算限制度量值。我们强调了与与平均场限制有关的全图差异及其转化为复杂汉堡部分差分差异的联系。
This paper is devoted to the study of the eigenvalues of the Wishart process which are the analogof the Dyson Brownian Motion for covariance matrices. Such processes were in particular studied byBru. The mean field convergence of the empirical measure of these eigenvalues was proved Malecki andPerez. In this paper, we provide a new approach to the mean field convergence problem using toolsfrom the free rectangular convolution theory developed by Benaych-Georges, which in particular allowsto compute explicitly the limit measure valued flow. We highlight the link with the integro-differentialequation related to the mean field limit and its translation into a complex Burgers partial differentialequation.
