标题： 具有奇异哈密顿量的吉布斯测度的大偏差及凯勒-爱因斯坦度量的出现 显示英文标题

标题： Large deviations for Gibbs measures with singular Hamiltonians and emergence of Kahler-Einstein metrics

摘要： 在本文和附带论文[9]中，通过采样“温度变形”的行列式点过程，引入了一种概率（统计力学）方法，用于在复代数流形X上构造规范度量。主要的新要素是针对具有奇异哈密顿量的吉布斯测度的大偏差原理，该原理在本文中得到了证明。作为应用，我们展示了在代数流形X上的规范点过程的大量粒子极限中，具有负曲率的Kähler-Einstein度量唯一出现。在附带论文[9]中，给出了到具有正Kodaira维数的代数流形X的扩展，并提出了一个关于负温度状态与具有正曲率的Kähler-Einstein度量存在性问题之间关系的猜想图景。 显示英文摘要

摘要： In the present paper and the companion paper [9] a probabilistic (statistical-mechanical) approach to the construction of canonical metrics on a complex algebraic varieties X is introduced, by sampling "temperature deformed" determinantal point processes. The main new ingredient is a large deviation principle for Gibbs measures with singular Hamiltonians, which is proved in the present paper. As an application we show that the unique Kahler-Einstein metric with negative Ricci curvature on a canonically polarized algebraic manifold X emerges in the many particle limit of the canonical point processes on X. In the companion paper [9] the extension to algebraic varieties X with positive Kodaira dimension is given and a conjectural picture relating negative temperature states to the existence problem for Kahler-Einstein metrics with positive Ricci curvature is developed.