# random matrices – Using linearization trick (free chance) to compute limiting spectral density of \$(XY+Z+A)(XY+Z+A)^high\$ retort

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## random matrices – Using linearization trick (free chance) to compute limiting spectral density of \$(XY+Z+A)(XY+Z+A)^high\$

Disclaimer. I solely began erudition the signify of free chance $$1$$ day in the past, and I’m quiet attempting to fullfil the basics, whereas making use of them to my avow particular issues arizing within the spectral evaluation of inescapable concrete random matrices.

Let $$X_{n,m}$$, $$Y_{m,ok}$$, $$Z_{m,ok}$$ breathe sizable impartial random matrices with entries from $$N(0,1)$$ and let $$A_{m,ok}$$ breathe a deterministic matrix. assume the random psd matrix $$R_{m,ok} := (X_{n,m}Y_{m,ok}+Z_{m,ok}+A_{m,ok})(X_{n,m}Y_{m,ok}+Z_{m,ok}+A_{m,ok})^high$$.

Question. How to make use of instruments from free chance (e.g the “linearization trick”, and so forth.) to compute the limiting spectral distribution of $$R_{m,ok}$$ ?

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