随机Loewner演化与Dyson圆系综
Stochastic Loewner Evolution and Dyson's Circular Ensembles
摘要：
引入随机Loewner演化（SLE_kappa）来描述二维临界系统中团簇边界的连续极限。我们证明了单位圆盘中N个径向SLEs的问题等价于圆盘边界上的Dyson布朗运动，参数β =4/kappa.结果，各种平衡临界模型给出了β不同于经典值1，2和4的圆系综的实现，它们对应于随机U（N）矩阵的对称类。一些散装临界指数相关的频谱相关的Calogero-Sutherland哈密顿量。主要结果也与共形场论的预言进行了比较。
英文摘要：
Stochastic Loewner Evolution (SLE_kappa) has been introduced as a description of the continuum limit of cluster boundaries in two-dimensional critical systems. We show that the problem of N radial SLEs in the unit disc is equivalent to Dyson's Brownian motion on the boundary of the disc, with parameter beta=4/kappa. As a result various equilibrium critical models give realisations of circular ensembles with beta different from the classical values of 1,2 and 4 which correspond to symmetry classes of random U(N) matrices. Some of the bulk critical exponents are related to the spectrum of the associated Calogero-Sutherland hamiltonian. The main result is also checked against the predictions of conformal field theory.
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