论文标题
在随机特征多项式时刻的临界临界时刻：GMC的观点
On the critical-subcritical moments of moments of random characteristic polynomials: a GMC perspective
论文作者
论文摘要
我们研究尺寸$ d \ leq 2 $的亚临界高斯乘法混乱（GMC）的“关键时刻”。特别是，我们为领先顺序渐近学建立了一个完全明确的公式，该公式与GMC的大偏差结果密切相关，并展示了相似的普遍性特征。我们猜想我们的结果正确地描述了随机矩阵时刻的类似矩的行为，或更一般的结构在整个介质量表中均非高斯并与对数相关。在圆形统一集合的设置中，对于整数情况进行了验证，扩展并加强了Claeys等人的结果。和法拉斯到高阶时刻。
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.
