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Acta Mathematica Sinica, English Series

, Volume 35, Issue 12, pp 1891–1905 | Cite as

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

  • Ming Chu GaoEmail author
Article
  • 8 Downloads

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.

Keywords

Bi-free central limit distributions non-Gaussian random matrices asymptotic bi-freeness 

MR(2010) Subject Classification

46L54 

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Copyright information

© Springer-Verlag GmbH Germany & The Editorial Office of AMS 2019

Authors and Affiliations

  1. 1.School of Mathematics and Information ScienceBaoji University of Arts and SciencesBaojiP. R. China
  2. 2.Department of MathematicsLouisiana CollegePinevilleUSA

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