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Phase Transitions for Products of Characteristic Polynomials under Dyson Brownian Motion

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Abstract

We study the averaged products of characteristic polynomials for the Gaussian and Laguerre β-ensembles with external source, and prove Pearcey-type phase transitions for particular full rank perturbations of source. The phases are characterised by determining the explicit functional forms of the scaled limits of the averaged products of characteristic polynomials, which are given as certain multidimensional integrals, with dimension equal to the number of products.

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Authors and Affiliations

  1. ARC Centre of Excellence for Mathematical and Statistical Frontiers, School of Mathematics and Statistics, The University of Melbourne, Victoria, 3010, Australia

    Peter J. Forrester

  2. CAS Key Laboratory of Wu Wen-Tsun Mathematics, School of Mathematical Sciences, University of Science and Technology of China, Hefei, 230026, P. R. China

    Dang-Zheng Liu

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  1. Peter J. Forrester
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  2. Dang-Zheng Liu
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Correspondence to Dang-Zheng Liu.

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Supported by Australian Research Council (Grant No. DP170102028), the National Natural Science Foundation of China (Grant No. 11771417) and the Youth Innovation Promotion Association CAS (Grant No. 2017491)

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Forrester, P.J., Liu, DZ. Phase Transitions for Products of Characteristic Polynomials under Dyson Brownian Motion. Acta. Math. Sin.-English Ser. 37, 509–524 (2021). https://doi.org/10.1007/s10114-020-9445-7

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  • DOI: https://doi.org/10.1007/s10114-020-9445-7

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