A constant regression characterization of the Marchenko– Pastur law

  1. Kamil Szpojankowski


In this paper, Lukacs type characterization of Marchenko–Pastur distribution in free probability is studied. We prove that for free X and Y, if conditional moments of order 1 and −1 of
(X + Y)−1/2X(X + Y)−1/2 given X + Y are constant, then X and Y follow the Marchenko–Pastur distribution.

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Probability and Mathematical Statistics

36, z. 1, 2016

Pages from 137 to 145

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