Non-Gaussian Random Bi-matrix Models for Bi-free Central Limit Distributions with Positive Definite Covariance Matrices
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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.
KeywordsBi-free central limit distributions non-Gaussian random matrices asymptotic bi-freeness
MR(2010) Subject Classification46L54
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