一族符合DOZZ公式的概率分布：关于二维GMC定律的一个猜想
A Family of Probability Distributions Consistent with the DOZZ Formula: Towards a Conjecture for the Law of 2D GMC
摘要：
构造概率分布的三参数族，使得其梅林变换被定义在与具有三个插入点$(α_1,α_2,α_3)$的黎曼球面上的2D GMC相同的域上，并且满足Kupiainen意义上的DOZZ公式（Ann.Math.191（2020）81 - 166）。族中的概率分布被定义为独立的Fyodorov-Bouchaud和$(2, 1)$和$(2, 2).$型Barnes β分布的幂的乘积。在特殊情况下的$α_1+α_2+α_3=2Q$的构造的概率分布是一致的与已知的小渐近偏差的二维GMC法律与处处正曲率。
英文摘要：
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.
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