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• W2109471867 abstract "Let $X$ be a random matrix whose squared singular value density is a polynomial ensemble. We derive double contour integral formulas for the correlation kernels of the squared singular values of $GX$ and $TX$, where $G$ is a complex Ginibre matrix and $T$ is a truncated unitary matrix. We also consider the product of $X$ and several complex Ginibre/truncated unitary matrices. As an application, we derive the precise condition for the squared singular values of the product of several truncated unitary matrices to follow a polynomial ensemble. We also consider the sum $H + M$ where $H$ is a GUE matrix and $M$ is a random matrix whose eigenvalue density is a polynomial ensemble. We show that the eigenvalues of $H + M$ follow a polynomial ensemble whose correlation kernel can be expressed as a double contour integral. As an application, we point out a connection to the two-matrix model." @default.
• W2109471867 created "2016-06-24" @default.
• W2109471867 creator A5044081911 @default.
• W2109471867 creator A5046454314 @default.
• W2109471867 creator A5051237961 @default.
• W2109471867 date "2015-05-04" @default.
• W2109471867 modified "2023-09-23" @default.
• W2109471867 title "Correlation kernels for sums and products of random matrices" @default.
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• W2109471867 doi "https://doi.org/10.48550/arxiv.1505.00610" @default.
• W2109471867 hasPublicationYear "2015" @default.
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