发表机构
The University of Hong Kong（香港大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出临界高斯乘性混沌的幂变差，通过重整化证明分数矩界与稳定收敛，统一解决正则性、谱及傅里叶衰减问题。
AI 中文摘要
我们引入了在任意维度中沿细化划分的临界高斯乘性混沌（GMC）的幂变差。在适当的重整化下，我们通过拉普拉斯变换估计证明了均匀分数矩界，以及向超临界GMC的稳定收敛。这些结果共同为临界混沌的正则性和谱问题提供了统一方法，得出：（i）对数模连续性的尖锐指数，（ii）临界刘维尔量子引力曲面非空本质谱的存在性；以及（iii）几乎必然的定量傅里叶衰减。
英文摘要
We introduce power variations of critical Gaussian multiplicative chaos (GMC) along refining partitions in arbitrary dimension. Under suitable renormalisation, we prove uniform fractional moment bounds via Laplace transform estimates as well as stable convergence to supercritical GMCs. Together, these results provide a unified approach to regularity and spectral questions for critical chaos, yielding: (i) the sharp exponent for the logarithmic modulus of continuity, (ii) the existence of non-empty essential spectrum for critical Liouville quantum gravity surfaces; and (iii) an almost-sure quantitative Fourier decay.
Comments33 pages; comments are welcome
