论文标题
从虚构的混乱中重建基本场
Reconstructing the base field from imaginary multiplicative chaos
论文作者
论文摘要
我们表明，假想的乘法混沌$ \ exp（iβγ）$确定了所有与log相关的高斯字段的基础字段$γ$的梯度，其形式为$ - \ log | x-y | + g（x，y）$具有$ g $的轻度规律条件，对于所有$ d \ geq 2 $，对于所有$β\ in（0，\ sqrt {d}）$。特别是，我们表明2D连续零边界高斯自由场是可测量的W.R.T.它的虚构混乱。
We show that the imaginary multiplicative chaos $\exp(iβΓ)$ determines the gradient of the underlying field $Γ$ for all log-correlated Gaussian fields with covariance of the form $-\log |x-y| + g(x,y)$ with mild regularity conditions on $g$, for all $d \geq 2$ and for all $β\in (0,\sqrt{d})$. In particular, we show that the 2D continuum zero boundary Gaussian free field is measurable w.r.t. its imaginary chaos.
