星标不变场的Liouville度量：尾和Weyl标度
Liouville metric of star-scale invariant fields: tails and Weyl scaling
摘要：
本文研究了具有短程关联的对数关联高斯场的Liouville度量。我们证明了在参数$γ_c >0$之下，具有不同长宽比的黎曼度量$e^{γϕ_{0,n}} ds^2$的矩形的左右长度以拟对数正态尾部集中，当$γ< \min ( γ_c, 0.4)$和连续极限与Weyl标度一致时，重整化度量是紧的.
英文摘要：
We study the Liouville metric associated to an approximation of a log-correlated Gaussian field with short range correlation. We show that below a parameter $γ_c >0$, the left-right length of rectangles for the Riemannian metric $e^{γϕ_{0,n}} ds^2$ with various aspect ratio is concentrated with quasi-lognormal tails, that the renormalized metric is tight when $γ< \min ( γ_c, 0.4)$ and that subsequential limits are consistent with the Weyl scaling.
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