Abstract
We use free probability to compute the limiting spectral properties of the harmonic mean of [Formula: see text] i.i.d. Wishart random matrices [Formula: see text] whose limiting aspect ratio is [Formula: see text] when [Formula: see text]. We demonstrate an interesting phenomenon where the harmonic mean [Formula: see text] of the [Formula: see text] Wishart matrices is closer in operator norm to [Formula: see text] than the arithmetic mean [Formula: see text] for small [Formula: see text], after which the arithmetic mean is closer. We also prove some results for the general case where the expectation of the Wishart matrices are not the identity matrix.
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