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- W3210522133 abstract "A family of random variables $mathbf{X}(s)$, depending on a real parameter $s>-frac{1}{2}$, appears in the asymptotics of the joint moments of characteristic polynomials of random unitary matrices and their derivatives, in the ergodic decomposition of the Hua-Pickrell measures and conjecturally in the asymptotics of the joint moments of Hardy's function and its derivative. Our first main result establishes a connection between the characteristic function of $mathbf{X}(s)$ and the $sigma$-Painlev'e III' equation in the full range of parameter values $s>-frac{1}{2}$. Our second main result gives the first explicit expression for the density and all the complex moments of the absolute value of $mathbf{X}(s)$ for integer values of $s$. Finally, we establish an analogous connection to another special case of the $sigma$-Painlev'e III' equation for the Laplace transform of the sum of the inverse points of the Bessel point process." @default.
- W3210522133 created "2021-11-08" @default.
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- W3210522133 date "2021-10-15" @default.
- W3210522133 modified "2023-09-24" @default.
- W3210522133 title "On a distinguished family of random variables and Painlevé equations" @default.
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- W3210522133 doi "https://doi.org/10.2140/pmp.2021.2.613" @default.
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