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Non-Gaussian Random Bi-matrix Models for Bi-free Central Limit Distributions with Positive Definite Covariance Matrices

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Abstract

In this paper, we construct random two-faced families of matrices with non-Gaussian entries to approximate a bi-free central limit distribution with a positive definite covariance matrix. We prove that, under modest conditions weaker than independence, a family of random two-faced families of matrices with non-Gaussian entries is asymptotically bi-free from a two-faced family of constant diagonal matrices.

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Authors and Affiliations

  1. School of Mathematics and Information Science, Baoji University of Arts and Sciences, Baoji, 721013, P. R. China

    Ming Chu Gao

  2. Department of Mathematics, Louisiana College, Pineville, LA, 71359, USA

    Ming Chu Gao

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  1. Ming Chu Gao
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Correspondence to Ming Chu Gao.

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Gao, M.C. Non-Gaussian Random Bi-matrix Models for Bi-free Central Limit Distributions with Positive Definite Covariance Matrices. Acta. Math. Sin.-English Ser. 35, 1891–1905 (2019). https://doi.org/10.1007/s10114-019-8345-1

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  • DOI: https://doi.org/10.1007/s10114-019-8345-1

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