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A family of probability distributions consistent with the DOZZ formula: towards a conjecture for the law of 2D GMC
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 $(\alpha_1,\alpha_2,\alpha_3)$ and satisfies the DOZZ formula in the sense of Kupiainen (Ann. Math. 191 (2020) 81 -- 166). …