LIMITING SPECTRAL DISTRIBUTIONS OF SUMS OF PRODUCTS OF NON-HERMITIAN RANDOM MATRICES

Kösters H, Tikhomirov A (2018)
PROBABILITY AND MATHEMATICAL STATISTICS-POLAND 38(2): 359-384.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Kösters, HolgerUniBi; Tikhomirov, Alexander
Abstract / Bemerkung
For fixed l >= 0 and m >= 1, let X-n((0)),X-n((1)), ... ,X-n((l)) be independent random n x n matrices with independent entries, let F-n((0)) := X-n((0)) (X-n((1)))(-1) ... (X-n((l)))(-1), and let F-n((1)), ... ,F-n((m)) be independent random matrices of the same form as F-n((0)). We show that as n -> infinity, the matrices F-n((0)) and m(-(l+1)/2) F-n((1)) + ... + F-n((m)) have the same limiting eigenvalue distribution. To obtain our results, we apply the general framework recently introduced in Gotze, Kosters, and Tikhomirov (2015) to sums of products of independent random matrices and their inverses. We establish the universality of the limiting singular value and eigenvalue distributions, and we provide a closer description of the limiting distributions in terms of free probability theory.
Erscheinungsjahr
2018
Zeitschriftentitel
PROBABILITY AND MATHEMATICAL STATISTICS-POLAND
Band
38
Ausgabe
2
Seite(n)
359-384
ISSN
0208-4147
Page URI
https://pub.uni-bielefeld.de/record/2933934

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Kösters H, Tikhomirov A. LIMITING SPECTRAL DISTRIBUTIONS OF SUMS OF PRODUCTS OF NON-HERMITIAN RANDOM MATRICES. PROBABILITY AND MATHEMATICAL STATISTICS-POLAND. 2018;38(2):359-384.
Kösters, H., & Tikhomirov, A. (2018). LIMITING SPECTRAL DISTRIBUTIONS OF SUMS OF PRODUCTS OF NON-HERMITIAN RANDOM MATRICES. PROBABILITY AND MATHEMATICAL STATISTICS-POLAND, 38(2), 359-384. doi:10.19195/0208-4147.38.2.6
Kösters, H., and Tikhomirov, A. (2018). LIMITING SPECTRAL DISTRIBUTIONS OF SUMS OF PRODUCTS OF NON-HERMITIAN RANDOM MATRICES. PROBABILITY AND MATHEMATICAL STATISTICS-POLAND 38, 359-384.
Kösters, H., & Tikhomirov, A., 2018. LIMITING SPECTRAL DISTRIBUTIONS OF SUMS OF PRODUCTS OF NON-HERMITIAN RANDOM MATRICES. PROBABILITY AND MATHEMATICAL STATISTICS-POLAND, 38(2), p 359-384.
H. Kösters and A. Tikhomirov, “LIMITING SPECTRAL DISTRIBUTIONS OF SUMS OF PRODUCTS OF NON-HERMITIAN RANDOM MATRICES”, PROBABILITY AND MATHEMATICAL STATISTICS-POLAND, vol. 38, 2018, pp. 359-384.
Kösters, H., Tikhomirov, A.: LIMITING SPECTRAL DISTRIBUTIONS OF SUMS OF PRODUCTS OF NON-HERMITIAN RANDOM MATRICES. PROBABILITY AND MATHEMATICAL STATISTICS-POLAND. 38, 359-384 (2018).
Kösters, Holger, and Tikhomirov, Alexander. “LIMITING SPECTRAL DISTRIBUTIONS OF SUMS OF PRODUCTS OF NON-HERMITIAN RANDOM MATRICES”. PROBABILITY AND MATHEMATICAL STATISTICS-POLAND 38.2 (2018): 359-384.

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