Eigenvalues of Product of Ginibre Ensembles and Their Inverses and that of Truncated Haar Unitary Matrices and Their Inverses
arxiv(2024)
摘要
Consider two types of products of independent random matrices, including
products of Ginibre matrices and inverse Ginibre matrices and products of
truncated Haar unitary matrices and inverse truncated Haar matrices. Each
product matrix has m multiplicands of n by n square matrices, and the
empirical distribution based on the n eigenvalues of the product matrix is
called empirical spectral distribution of the matrix. In this paper, we
investigate the limiting empirical spectral distribution of the product
matrices when n tends to infinity and m changes with n. For properly
rescaled eigenvalues for two types of the product matrices, we obtain the
necessary and sufficient conditions for the convergence of the empirical
spectral distributions.
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