模高斯收敛：概率论和数论中的新极限定理
Mod-Gaussian convergence: new limit theorems in probability and number theory
摘要：
我们引入一种新的类型的依概率收敛理论，我们称之为“模高斯收敛”。它直接受到随机矩阵理论和数论中关于特征多项式或zeta函数值的矩的定理和公式的启发。我们详细研究了这种类型的收敛的框架中的无限可分分布，并展示了一些无条件的发生在数论，特别是家庭的$L$ -功能在功能领域的卡茨Sarnak框架。类似的“mod-Poisson收敛”现象也出现在经典的Erdens-Kác定理中。
英文摘要：
We introduce a new type of convergence in probability theory, which we call ``mod-Gaussian convergence''. It is directly inspired by theorems and conjectures, in random matrix theory and number theory, concerning moments of values of characteristic polynomials or zeta functions. We study this type of convergence in detail in the framework of infinitely divisible distributions, and exhibit some unconditional occurrences in number theory, in particular for families of $L$-functions over function fields in the Katz-Sarnak framework. A similar phenomenon of ``mod-Poisson convergence'' turns out to also appear in the classical Erdős-Kác Theorem.
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