For the q-Al-Salam-Carlitz unitary ensemble with a<0, the authors derive explicit spectral moments and a limiting density with two soft-to-hard edge phase transitions.
Moments of discrete classical $q$-orthogonal polynomial ensembles
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abstract
We consider some discrete $q$-analogues of the classical continuous orthogonal polynomial ensembles. Building on results due to Morozov, Popolitov and Shakirov, we find representations for the moments of the discrete $q$-Hermite and discrete $q$-Laguerre ensembles in terms of basic hypergeometric series. We find that when the number of particles is suitably randomised, the moments may be represented as basic hypergeometric orthogonal polynomials, with corresponding three-term recurrences in $k$, the order of the moments.
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Spectral analysis of $q$-deformed unitary ensembles with the Al-Salam--Carlitz weight
For the q-Al-Salam-Carlitz unitary ensemble with a<0, the authors derive explicit spectral moments and a limiting density with two soft-to-hard edge phase transitions.