Distribution of Eigenvalues of Sample Covariance Matrices with Tensor Product Samples
We consider the n² × n² real symmetric and hermitian matrices Mₙ, which are equal to the sum mn of tensor products of the vectors Xμ = B(Yμ ⊗ Yμ), μ = 1, . . . ,mn, where Yμ are i.i.d. random vectors from Rⁿ(Cⁿ) with zero mean and unit variance of components, and B is an n² × n² positive definite no...
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| Veröffentlicht in: | Журнал математической физики, анализа, геометрии |
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| Datum: | 2017 |
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| Sprache: | Englisch |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2017
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/140566 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Distribution of Eigenvalues of Sample Covariance Matrices with Tensor Product Samples / D. Tieplova // Журнал математической физики, анализа, геометрии. — 2017. — Т. 13, № 1. — С. 82-98. — Бібліогр.: 11 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862748996124016640 |
|---|---|
| author | Tieplova, D. |
| author_facet | Tieplova, D. |
| citation_txt | Distribution of Eigenvalues of Sample Covariance Matrices with Tensor Product Samples / D. Tieplova // Журнал математической физики, анализа, геометрии. — 2017. — Т. 13, № 1. — С. 82-98. — Бібліогр.: 11 назв. — англ. |
| collection | DSpace DC |
| container_title | Журнал математической физики, анализа, геометрии |
| description | We consider the n² × n² real symmetric and hermitian matrices Mₙ, which are equal to the sum mn of tensor products of the vectors Xμ = B(Yμ ⊗ Yμ), μ = 1, . . . ,mn, where Yμ are i.i.d. random vectors from Rⁿ(Cⁿ) with zero mean and unit variance of components, and B is an n² × n² positive definite non-random matrix. We prove that if mₙ / n² → c ∊ [0,+∞) and the Normalized Counting Measure of eigenvalues of BJB, where J is defined below in (2.6), converges weakly, then the Normalized Counting Measure of eigenvalues of Mn converges weakly in probability to a non-random limit, and its Stieltjes transform can be found from a certain functional equation.
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| first_indexed | 2025-12-07T20:57:22Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-140566 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1812-9471 |
| language | English |
| last_indexed | 2025-12-07T20:57:22Z |
| publishDate | 2017 |
| publisher | Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| record_format | dspace |
| spelling | Tieplova, D. 2018-07-10T17:04:04Z 2018-07-10T17:04:04Z 2017 Distribution of Eigenvalues of Sample Covariance Matrices with Tensor Product Samples / D. Tieplova // Журнал математической физики, анализа, геометрии. — 2017. — Т. 13, № 1. — С. 82-98. — Бібліогр.: 11 назв. — англ. 1812-9471 DOI: doi.org/10.15407/mag13.01.082 Mathematics Subject Classification 2000: 15B52 https://nasplib.isofts.kiev.ua/handle/123456789/140566 We consider the n² × n² real symmetric and hermitian matrices Mₙ, which are equal to the sum mn of tensor products of the vectors Xμ = B(Yμ ⊗ Yμ), μ = 1, . . . ,mn, where Yμ are i.i.d. random vectors from Rⁿ(Cⁿ) with zero mean and unit variance of components, and B is an n² × n² positive definite non-random matrix. We prove that if mₙ / n² → c ∊ [0,+∞) and the Normalized Counting Measure of eigenvalues of BJB, where J is defined below in (2.6), converges weakly, then the Normalized Counting Measure of eigenvalues of Mn converges weakly in probability to a non-random limit, and its Stieltjes transform can be found from a certain functional equation. en Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України Журнал математической физики, анализа, геометрии Distribution of Eigenvalues of Sample Covariance Matrices with Tensor Product Samples Article published earlier |
| spellingShingle | Distribution of Eigenvalues of Sample Covariance Matrices with Tensor Product Samples Tieplova, D. |
| title | Distribution of Eigenvalues of Sample Covariance Matrices with Tensor Product Samples |
| title_full | Distribution of Eigenvalues of Sample Covariance Matrices with Tensor Product Samples |
| title_fullStr | Distribution of Eigenvalues of Sample Covariance Matrices with Tensor Product Samples |
| title_full_unstemmed | Distribution of Eigenvalues of Sample Covariance Matrices with Tensor Product Samples |
| title_short | Distribution of Eigenvalues of Sample Covariance Matrices with Tensor Product Samples |
| title_sort | distribution of eigenvalues of sample covariance matrices with tensor product samples |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/140566 |
| work_keys_str_mv | AT tieplovad distributionofeigenvaluesofsamplecovariancematriceswithtensorproductsamples |