2020/08/05 by Dmitry Ostrovsky
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Advanced Mathematical Identities #Alpha (finance) #Complex Systems and Time Series Analysis #Conjecture #Convolution of probability distributions #Curvature #Distribution (mathematics) #Domain (mathematical analysis) #Financial Risk and Volatility Modeling #Geometry #Mathematical analysis #Mathematics #Moment-generating function #Probability distribution #Pure mathematics #Random Matrices and Applications #Random variable #Statistics #Stochastic processes and financial applications #advanced mathematical theories #math-ph #math.MP #math.PR #msc:60D99 #msc:60E07 #msc:60E10 #msc:81T20 #msc:81T40
paper · pdf · doi:10.2140/pmp.2021.2.533
published as Prob. Math. Phys. 2 (2021) 533-562 · 30 pages, revised version, to appear in PMP
openalex publication_date 2020/08/05 · arxiv created 2021/04/05 · arxiv updated 2021/11/03 · openalex created_date 2021/11/08 · openalex updated_date 2026/08/05
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 (α1,α2,α3) 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 α1+α2+α3=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.