关于随机特征多项式的矩的矩的临界-次临界时刻：GMC视角
On the critical-subcritical moments of moments of random characteristic polynomials: a GMC perspective
AI总结：
本文从GMC视角研究了 $d \leq 2$ 维下次临界高斯乘性混沌的临界矩，给出了首阶渐近的显式公式，并在圆酉系综整数情形下验证了其对随机矩阵矩的矩行为的普适性描述。
摘要：
我们研究了 $d \leq 2$ 维下次临界高斯乘性混沌（GMCs）的“临界矩”。特别地，我们建立了一个完全显式的首阶渐近公式，该公式与 GMCs 的大偏差结果密切相关，并展现出相似的普适性特征。我们推测，我们的结果正确描述了随机矩阵的矩的矩，或更一般地，在整个介观尺度上渐近高斯且对数相关的结构的类似行为。这在圆酉系综（circular unitary ensemble）的整数情形下得到了验证，扩展并加强了 Claeys 等人和 Fahs 的结果至高阶矩。
英文摘要：
We study the 'critical moments' of subcritical Gaussian multiplicative chaos (GMCs) in dimensions $d \leq 2$. In particular, we establish a fully explicit formula for the leading order asymptotics, which is closely related to large deviation results for GMCs and demonstrates a similar universality feature. We conjecture that our result correctly describes the behaviour of analogous moments of moments of random matrices, or more generally structures which are asymptotically Gaussian and log-correlated in the entire mesoscopic scale. This is verified for an integer case in the setting of circular unitary ensemble, extending and strengthening the results of Claeys et al. and Fahs to higher-order moments.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
