Abstract
We establish the asymptotics of the joint moments of the characteristic polynomial of a random unitary matrix and its derivative for general real values of the exponents, proving a conjecture made by Hughes in 2001. Moreover, we give a probabilistic representation for the leading order coefficient in the asymptotic in terms of a realvalued random variable that plays an important role in the ergodic decomposition of the HuaPickrell measures. This enables us to establish connections between the characteristic function of this random variable and the σPainlevé III' equation.
Original language  English 

Publisher  ArXiv 
Number of pages  32 
Publication status  Published  28 May 2020 
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Theo Assiotis
 School of Mathematics  Lectureship/Readership in Probability and Stochastic Analysi
Person: Academic: Research Active (Teaching)