Gaussian unitary ensemble with jump discontinuities and the coupled Painlev\'e II and IV systems

27 Feb 2020 Wu Xiao-Bo Xu Shuai-Xia

We study the orthogonal polynomials and the Hankel determinants associated with Gaussian weight with two jump discontinuities. When the degree $n$ is finite, the orthogonal polynomials and the Hankel determinants are shown to be connected to the coupled Painlev\'e IV system... (read more)

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  • CLASSICAL ANALYSIS AND ODES