论文标题
来自对数相关场的厚点的乘法混乱度量
Multiplicative chaos measures from thick points of log-correlated fields
论文作者
论文摘要
我们证明，可以从基础对数相关场的极端水平集或厚点构建乘法混乱度量。我们开发了一种涵盖整个亚临界阶段的方法，并且仅需要对该场的合适指数力矩的渐近学。作为一种应用，我们使用已知的toeplitz noctotics（与（合并）Fisher-Hartwig奇异性的toeplitz确定因素）确定了HAAR分布式随机单位矩阵（CUE）的绝对多项式的对数的这些估计值。因此，这证明了fyodorov的猜想和基地组织，即提示特征多项式的厚点的波动。
We prove that multiplicative chaos measures can be constructed from extreme level sets or thick points of the underlying logarithmically correlated field. We develop a method which covers the whole subcritical phase and only requires asymptotics of suitable exponential moments for the field. As an application, we establish these estimates hold for the logarithm of the absolute value of the characteristic polynomial of a Haar distributed random unitary matrix (CUE), using known asymptotics for Toeplitz determinant with (merging) Fisher-Hartwig singularities. Hence, this proves a conjecture of Fyodorov and Keating concerning the fluctuations of the volume of thick points of the CUE characteristic polynomial.
