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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:

  1. https://www.math.wisc.edu/~valko/courses/833/2009f/lec_6_7.pdf

  2. https://galton.uchicago.edu/~lalley/Courses/386/Wigner.pdf

  3. https://ion.nechita.net/wp-content/uploads/2016/02/using-rm-in-qit.pdf

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