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Precise Deviations for Discrete Ensembles

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Abstract

We consider precise deviations for discrete ensembles. For β = 2 case, we first establish an asymptotic formula of the Christoffel–Darboux kernel of the discrete orthogonal polynomials on an infinite regular lattice with weight e−NV(x). Then we use the asymptotic formula to get the precise deviations of the extreme value for corresponding ensemble.

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Acknowledgements

The authors thank the referees for valuable comments and suggestions.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, P. R. China

    Wen Xuan Chen & Fu Qing Gao

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  1. Wen Xuan Chen
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  2. Fu Qing Gao
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Correspondence to Fu Qing Gao.

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Supported by the National Natural Science Foundation of China (Grant Nos. 11971361, 11731012)

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Chen, W.X., Gao, F.Q. Precise Deviations for Discrete Ensembles. Acta. Math. Sin.-English Ser. 39, 1580–1596 (2023). https://doi.org/10.1007/s10114-023-1570-7

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  • DOI: https://doi.org/10.1007/s10114-023-1570-7

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