Limiting spectral distributions of sums of products of non-Hermitian random matrices

Kösters, H.; Tikhomirov, A.

doi:10.19195/0208-4147.38.2.6

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Tytuł artykułu

Limiting spectral distributions of sums of products of non-Hermitian random matrices

Autorzy

Kösters H. , Tikhomirov A.

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DOI

10.19195/0208-4147.38.2.6

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Abstrakty

For fixed l ≥ 0 and m ≥ 1, let X⁽⁰⁾_n, X⁽¹⁾_n,…, X^(l)_n be independent random n × n matrices with independent entries, let F⁽⁰⁾_n:= X⁽⁰⁾_n (X^(l)_n)⁻¹…(X^(l)_n)⁻¹, and let F⁽¹⁾_n,…, F^(m)_n be independent random matrices of the same form as F⁽⁰⁾_n. We show that as n → ∞, the matrices F⁽⁰⁾_n and m^−(l+1)/2 (F⁽¹⁾_n + … + F^(m)_n) have the same limiting eigenvalue distribution. To obtain our results, we apply the general framework recently introduced in Götze, Kösters, 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 pro vide a closer description of the limiting distributions in terms of free probabilisty theory.

Słowa kluczowe

non-Hermitian random matrices limiting spectral distributions free probability theory stable distributions

Wydawca

Wrocław University of Science and Technology

Czasopismo

Probability and Mathematical Statistics

Rocznik

2018

Tom

Vol. 38, Fasc. 2

Strony

359--384

Opis fizyczny

Bibliogr. 38 poz.

Twórcy

autor

Kösters H.

hkoesters@math.uni-bielefeld.de

Department of Mathematics, Bielefeld University, Germany

autor

Tikhomirov A.

antikhom51@gmail.com

Institute of Physics and Mathematics, Komi Science Center of Ural Division of RAS, Syktyvkar State University, Russia

Bibliografia

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Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).

Typ dokumentu

Bibliografia

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