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- W3100697790 abstract "In this paper, we study random matrix models which are obtained as a non-commutative polynomial in random matrix variables of two kinds: (a) a first kind which have a discrete spectrum in the limit, (b) a second kind which have a joint limiting distribution in Voiculescu's sense and are globally rotationally invariant. We assume that each monomial constituting this polynomial contains at least one variable of type (a), and show that this random matrix model has a set of eigenvalues that almost surely converges to a deterministic set of numbers that is either finite or accumulating to only zero in the large dimension limit. For this purpose we define a framework (cyclic monotone independence) for analyzing discrete spectra and develop the moment method for the eigenvalues of compact (and in particular Schatten class) operators. We give several explicit calculations of discrete eigenvalues of our model." @default.
- W3100697790 created "2020-11-23" @default.
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- W3100697790 date "2018-07-01" @default.
- W3100697790 modified "2023-10-03" @default.
- W3100697790 title "Free probability for purely discrete eigenvalues of random matrices" @default.
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- W3100697790 doi "https://doi.org/10.2969/jmsj/77147714" @default.
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