Universal sum and product rules for random matrices

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Abstract

The spectral density of random matrices is studied through a quaternionic generalisation of the Green's function, which precisely describes the mean spectral density of a given matrix under a particular type of random perturbation. Exact and universal expressions are found in the high-dimension limit for the quaternionic Green's functions of random matrices with independent entries when summed or multiplied with deterministic matrices. From these, the limiting spectral density can be accurately predicted.
Original languageEnglish
Article number093304
Number of pages15
JournalJournal of Mathematical Physics
Volume51
Issue number9
Early online date26 Sep 2010
DOIs
Publication statusPublished - Sep 2010

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