随机乘性函数产生的乘性混沌
Multiplicative chaos from random multiplicative functions
AI总结：
本研究从扭曲斯坦豪斯乘性函数的狄利克雷级数构造乘性混沌测度，通过新颖部分求和技巧证明其普适性，还证明其与GMC测度几乎必然相互绝对连续，统一扩展了Gorodetsky与Wong的相关结果。
AI中文摘要：
我们从扭曲斯坦豪斯（Steinhaus）乘性函数的狄利克雷级数出发，构造了乘性混沌测度。本研究有三个主要特点：第一，我们的论证同时处理了整个亚临界和临界阶段；第二，我们证明，当素数截断趋向无穷大且以任意速度从右侧逼近临界线时，狄利克雷级数的任意近似都会产生相同的乘性混沌测度，这类结果被称为“普适性”结果，我们通过一种新颖且快速的部分求和技巧证明了这一点；第三，我们证明，在同一概率空间上耦合的乘性混沌测度，与同一阶段的高斯乘性混沌（GMC）测度几乎必然相互绝对连续。本研究统一并扩展了Gorodetsky与Wong近期突破性三篇系列论文中的结果。
英文摘要：
We construct the multiplicative chaos measures emerging from the Dirichlet series of the twisted Steinhaus multiplicative function. Our work has three main features. First, our argument treats the full subcritical and critical phases simultaneously. Second, we show that the same multiplicative chaos measure arises from any approximation to the Dirichlet series in which the prime cutoff is sent to infinity and the critical line is approached from the right at arbitrary speeds. Such results are known as "universality" results, and we show this via a novel and quick partial summation trick. Third, we show that the multiplicative chaos measure is mutually absolutely continuous with a GMC measure in the same phase, coupled on the same probability space, almost surely. Our work unifies and extends results from a recent breakthrough trilogy of papers by Gorodetsky and Wong.
