论文标题
亚临界复杂高斯乘法混乱的普遍性
A universality result for subcritical Complex Gaussian Multiplicative Chaos
论文作者
论文摘要
在本文中，我们表明（在一些较小的技术假设下）复杂的高斯乘法混乱定义为被定义为$ \ log $ - 相关的高斯磁场的复杂指数，可以通过取得平滑核的卷曲场的指数的限制来获得。我们考虑了两种类型的混乱：对于日志相关的字段$ x $和$ e^{γx} $，$γ=α+Iβ$，$α，$α，β\ in \ Mathbb r $ in \ Mathbb r $和$ e^{αx+iβY} $ for $ x $ for $ x $和$ y $ y $ $ $ $ $ $ a $α，β\ nmath $ \ nmath $ \ in $ \ in $ \ in。我们的结果在范围内有效 $ \ MATHCAL O _ {\ MATHRM {sub}}：= \ {α^2+β^2+β^2 <d \} \ cup \ cup \ {|α| \ in（\ sqrt {d/2}，\ sqrt {d/2}，\ sqrt {2d}） \}，直到边界的$$猜想是最佳的。
In the present paper, we show that (under some minor technical assumption) Complex Gaussian Multiplicative Chaos defined as the complex exponential of a $\log$-correlated Gaussian field can be obtained by taking the limit of the exponential of the field convoluted with a smoothing Kernel. We consider two types of chaos: $e^{γX}$ for a log correlated field $X$ and $γ=α+iβ$, $α, β\in \mathbb R$ and $e^{αX+iβY}$ for $X$ and $Y$ two independent fields with $α, β\in \mathbb R$. Our result is valid in the range $$ \mathcal O_{\mathrm{sub}}:=\{ α^2+β^2<d \} \cup \{ |α|\in (\sqrt{d/2},\sqrt{2d} ) \text{ and } |β|< \sqrt{2d}-|α| \},$$ which, up to boundary, is conjectured to be optimal.
