# Products of Independent Quaternion Ginibre Matrices and their Correlation Functions

Ipsen J (2013) *J. Phys. A: Math. Theor.* 46(26): 265201.

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We discuss the product of independent induced quaternion ($\beta=4$) Ginibrematrices, and the eigenvalue correlations of this product matrix. The jointprobability density function for the eigenvalues of the product matrix is shownto be identical to that of a single Ginibre matrix, but with a more complicatedweight function. We find the skew-orthogonal polynomials corresponding to theweight function of the product matrix, and use the method of skew-orthogonalpolynomials to compute the eigenvalue correlation functions for productmatrices of finite size. The radial behavior of the density of states isstudied in the limit of large matrices, and the macroscopic density isdiscussed. The microscopic limit at the origin, at the edge(s) and in the bulkis also discussed for the radial behavior of the density of states.

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Ipsen J. Products of Independent Quaternion Ginibre Matrices and their Correlation Functions.

*J. Phys. A: Math. Theor.*2013;46(26):265201.Ipsen, J. (2013). Products of Independent Quaternion Ginibre Matrices and their Correlation Functions.

*J. Phys. A: Math. Theor.*,*46*(26), 265201. doi:10.1088/1751-8113/46/26/265201Ipsen, J. (2013). Products of Independent Quaternion Ginibre Matrices and their Correlation Functions.

*J. Phys. A: Math. Theor.*46, 265201.Ipsen, J., 2013. Products of Independent Quaternion Ginibre Matrices and their Correlation Functions.

*J. Phys. A: Math. Theor.*, 46(26), p 265201. J. Ipsen, “Products of Independent Quaternion Ginibre Matrices and their Correlation Functions”,

*J. Phys. A: Math. Theor.*, vol. 46, 2013, pp. 265201. Ipsen, J.: Products of Independent Quaternion Ginibre Matrices and their Correlation Functions. J. Phys. A: Math. Theor. 46, 265201 (2013).

Ipsen, Jesper. “Products of Independent Quaternion Ginibre Matrices and their Correlation Functions”.

*J. Phys. A: Math. Theor.*46.26 (2013): 265201.
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arXiv 1301.3343