论文标题
从非交换几何到随机矩阵理论
From Noncommutative Geometry to Random Matrix Theory
论文作者
论文摘要
我们回顾了非交通性几何形状建议的随机矩阵模型的分析研究中的最新进展。一个人考虑了模糊的光谱三元，其中可能的狄拉克运算符的空间被分配了概率分布。这些狄拉克运算符的集合被构造为有限非交通空间上欧几里得量子重力的玩具模型，并显示了许多有趣的属性。这些集合表现出光谱相变，它们在这些相变的附近显示出歧管样行为。在某些情况下，人们可以在双缩放限制中恢复liouville量子重力。我们重点介绍了bootstrap技术，库仑气体方法和拓扑递归的示例。
We review recent progress in the analytic study of random matrix models suggested by noncommutative geometry. One considers fuzzy spectral triples where the space of possible Dirac operators is assigned a probability distribution. These ensembles of Dirac operators are constructed as toy models of Euclidean quantum gravity on finite noncommutative spaces and display many interesting properties. The ensembles exhibit spectral phase transitions, and near these phase transitions they show manifold-like behavior. In certain cases one can recover Liouville quantum gravity in the double scaling limit. We highlight examples where bootstrap techniques, Coulomb gas methods, and Topological Recursion are applicable.
