论文标题
$（1+ \ varepsilon）$ - 足以表征GFF
$(1+\varepsilon)$-moments suffice to characterise the GFF
论文作者
论文摘要
我们表明，从以下意义上讲，“没有稳定的索引$α\的自由领域”。作者在先前的作品中证明了这是\ emph {第四矩假设}的约束，在平面的域上$ d $上的任何随机广义函数，满足的保形不变性和天然域马尔可夫属性，必须是高斯自由场的常数倍数。在本文中，我们表明存在$（1+ \ varepsilon）$ - 矩就足以结论相同的结论。一个关键的想法是一种探索该领域的新方法，在这里（而不是查看更标准的圆平均），我们从边界开始，并发现该领域的平均值相对于一定的“击球密度”。
We show that there is "no stable free field of index $α\in (1,2)$", in the following sense. It was proved in a previous work by the authors, that subject to a \emph{fourth moment assumption}, any random generalised function on a domain $D$ of the plane, satisfying conformal invariance and a natural domain Markov property, must be a constant multiple of the Gaussian free field. In this article we show that the existence of $(1+\varepsilon)$-moments is sufficient for the same conclusion. A key idea is a new way of exploring the field, where (instead of looking at the more standard circle averages) we start from the boundary and discover averages of the field with respect to a certain "hitting density" of Itô excursions.
