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Discrete orthogonal ensemble on the exponential lattices

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arxiv 2206.08633 v1 pith:TNAX7NV2 submitted 2022-06-17 math-ph math.MP

Peter J Forrester , Shi-Hao Li , Bo-Jian Shen , Guo-Fu Yu This is my paper · ORCID
classification math-phmath.MP
keywords ensembleorthogonalskewconsideredexponentialjacobisymmetrical-salam
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abstract

Inspired by Aomoto's $q$-Selberg integral, the orthogonal ensemble in the exponential lattice is considered in this paper. By introducing a skew symmetric kernel, the configuration space of this ensemble is constructed to be symmetric and thus, corresponding skew inner product, skew orthogonal polynomials as well as correlation functions are explicitly formulated. Examples including Al-Salam & Carlitz, $q$-Laguerre, little $q$-Jacobi and big $q$-Jacobi cases are considered.

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  1. Spectral analysis of $q$-deformed unitary ensembles with the Al-Salam--Carlitz weight

    math-ph 2025-07 conditional novelty 6.0 of 10

    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.

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