论文标题
与Dozz公式一致的概率分布的家族：朝着2D GMC法律的猜想
A Family of Probability Distributions Consistent with the DOZZ Formula: Towards a Conjecture for the Law of 2D GMC
论文作者
论文摘要
构建了一个三个概率分布的参数家族，以使其Mellin变换与Riemann Sphere上的2D GMC相同的领域定义，并具有三个插入点$（α_1，α_2，α_3）$（α_1，α_2，α_3）$，并满足kupiainen（Ann。Math。191（2020）81-166）的DOZZ公式。家庭中的概率分布被定义为独立的Fyodorov-Bouchaud和Barnes Beta型$（2，1）$（2，1）$和$（2，2）的能力。在特殊情况下，$ $ $α_1+α_1+α_2+α_3= 2q $ $ cants显示了与已知的小型驱动器相一致的构造概率分布与2D gmc cul a cul cul cul cul cul a and 2d gmc一致。
A three parameter family of probability distributions is constructed such that its Mellin transform is defined over the same domain as the 2D GMC on the Riemann sphere with three insertion points $(α_1,α_2,α_3)$ and satisfies the DOZZ formula in the sense of Kupiainen (Ann. Math. 191 (2020) 81 -- 166). The probability distributions in the family are defined as products of independent Fyodorov-Bouchaud and powers of Barnes beta distributions of types $(2, 1)$ and $(2, 2).$ In the special case of $α_1+α_2+α_3=2Q$ the constructed probability distribution is shown to be consistent with the known small deviation asymptotic of the 2D GMC laws with everywhere positive curvature.
