On a distinguished family of random variables and Painlevé equations
On a distinguished family of random variables and Painlevé equations
A family of random variables X(s), depending on a real parameter s > -1 2 , appears in the asymptotics of the joint moments of characteristic polynomials of random unitary matrices and their derivatives [5], in the ergodic decomposition of the Hua-Pickrell measures [12], [59] and conjecturally in the asymptotics …