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- W4299552010 abstract "For fixed positive integers m, we consider the product of m independent n by n random matrices with iid entries as in the limit as n tends to infinity. Under suitable assumptions on the entries of each matrix, it is known that the limiting empirical distribution of the eigenvalues is described by the m-th power of the circular law. Moreover, this same limiting distribution continues to hold if each iid random matrix is additively perturbed by a bounded rank deterministic error. However, the bounded rank perturbations may create one or more outlier eigenvalues. We describe the asymptotic location of the outlier eigenvalues, which extends a result of Terence Tao for the case of a single iid matrix. Our methods also allow us to consider several other types of perturbations, including multiplicative perturbations." @default.
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- W4299552010 date "2017-11-20" @default.
- W4299552010 modified "2023-09-30" @default.
- W4299552010 title "Outliers in the spectrum for products of independent random matrices" @default.
- W4299552010 doi "https://doi.org/10.48550/arxiv.1711.07420" @default.
- W4299552010 hasPublicationYear "2017" @default.
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