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Convergence of high dimensional Toeplitz and related matrices with correlated inputs
Kartick Adhikari, Arup Bose, Shambhu Nath Maurya · 2023-10-05 · via math.PR updates on arXiv.org

We investigate the joint convergence of independent random Toeplitz matrices with complex input entries that have a pair-correlation structure, along with deterministic Toeplitz matrices and the backward identity permutation matrix. Further, we study the joint convergence of independent generalized Toeplitz matrices along with other related matrices. The limits depend only on the correlation structure but are universal otherwise, in that they do not depend on the underlying distributions of the entries. In particular, these results provide the joint convergence of asymmetric Hankel matrices. Earlier results in the literature on the joint convergence of random symmetric Toeplitz and symmetric Hankel matrices with real entries follow as special cases.

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