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

Non-Gaussian Random Bi-matrix Models for Bi-free Central Limit Distributions with Positive Definite Covariance Matrices
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摘要 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. 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.
作者 Ming Chu GAO
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2019年第12期1891-1905,共15页 数学学报(英文版)
关键词 Bi-free CENTRAL limit distributions NON-GAUSSIAN RANDOM matrices asymptotic bi-freeness Bi-free central limit distributions non-Gaussian random matrices asymptotic bi-freeness
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