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Contents of PMS, Vol. 36, Fasc. 1,
pages 137 - 145
 

A CONSTANT REGRESSION CHARACTERIZATION OF THE MARCHENKO–PASTUR LAW

Kamil Szpojankowski

Abstract: 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.

2000 AMS Mathematics Subject Classification: Primary: 46L54; Secondary: 62E10.

Keywords and phrases: Lukacs characterization, free Poisson distribution, free cumulants.

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