Do you happen to know a reference for exercise 2.1.18 from page 20 of Zeitouni's et al textbook: http://www.wisdom.weizmann.ac.il/~zeitouni/cupbook.pdf ?
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This exercise develops the proof of the Marchenko-Pastur distribution. Worked out proofs along similar lines can be found at various places, some pointers follow. None of these take precisely the same steps as in the exercise, but I presume once you have understood one of these worked out proofs you're done:
answered Nov 11, 2017 at 22:15
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$\begingroup$ I found the paper itself of Marcenko - Pastur: ipgold.epfl.ch/~leveque/Matrix/marchenko_pastur.pdf $\endgroup$– AlanCommented Dec 1, 2017 at 16:55