标题： 经典β系综和高温下的相关特征值过程以及马尔可夫-克雷因变换 显示英文标题

标题： Classical beta ensembles and related eigenvalues processes at high temperature and the Markov--Krein transform

摘要： 本文的目的是通过使用马尔可夫-克雷因变换，在高温区域内识别实线上经典β系综及其相关特征值过程的极限。 我们证明了高斯β系综（分别对应β拉盖尔系综和β雅可比系综）的极限测度是高斯分布（分别对应伽马分布和β分布）的逆马尔可夫-克雷因变换。 在过程层面，我们证明了极限概率测度值过程是某个一维随机过程的逆马尔可夫-克雷因变换。 显示英文摘要

摘要： The aim of this paper is to identify the limit in a high temperature regime of classical beta ensembles on the real line and related eigenvalue processes by using the Markov--Krein transform. We show that the limiting measure of Gaussian beta ensembles (resp.\ beta Laguerre ensembles and beta Jacobi ensembles) is the inverse Markov--Krein transform of the Gaussian distribution (resp.\ the gamma distribution and the beta distribution). At the process level, we show that the limiting probability measure-valued process is the inverse Markov--Krein transform of a certain 1d stochastic process.