标题： 经典贝塔系综及相关高温度下的特征值过程和马科夫-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： 本文的目的是利用马尔可夫-克雷因变换来确定实线上经典贝塔系综在高温极限下的极限以及相关特征值过程。我们证明了高斯贝塔系综（分别地，贝塔拉盖尔系综和贝塔雅可比系综）的极限测度是高斯分布（分别地，伽玛分布和贝塔分布）的逆马尔可夫-克雷因变换。在过程水平上，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.