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A functional limit theorem for the empirical measure-valued process ofeigenvalues of a matrix fractional Brownian motion is obtained. It is shownthat the limiting measure-valued process is the non-commutative fractionalBrownian motion recently introduced by Nourdin and Taqqu. Young and Skorohodstochastic integral techniques and fractional calculus are the main tools used.

A Random Matrix Approximation for the Non-commutative Fractional Brownian Motion