A result on the limiting spectral distribution of random matrices with unequal variance entries
Abstract A classical result in random matrix theory reveals that the limiting spectral distribution of a Wigner matrix whose entries have a common variance and satisfy other regular assumptions almost surely converges to the semicircular law. In the paper, we will relax the assumption of uniform cov...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2020-06-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13660-020-02440-7 |
| _version_ | 1818176731200094208 |
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| author | Shaojia Jin Junshan Xie |
| author_facet | Shaojia Jin Junshan Xie |
| author_sort | Shaojia Jin |
| collection | DOAJ |
| description | Abstract A classical result in random matrix theory reveals that the limiting spectral distribution of a Wigner matrix whose entries have a common variance and satisfy other regular assumptions almost surely converges to the semicircular law. In the paper, we will relax the assumption of uniform covariance of each entry, when the average of the normalized sums of the variances in each row of the data matrix converges to a constant, we prove that the same limiting spectral distribution holds. A similar result on a sample covariance matrix is also established. The proofs mainly depend on the Stein equation and the generalized Stein equation of independent random variables. |
| first_indexed | 2024-12-11T20:20:51Z |
| format | Article |
| id | doaj.art-8adae1df585440b0b7fef376249fa436 |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-12-11T20:20:51Z |
| publishDate | 2020-06-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-8adae1df585440b0b7fef376249fa4362022-12-22T00:52:04ZengSpringerOpenJournal of Inequalities and Applications1029-242X2020-06-012020111310.1186/s13660-020-02440-7A result on the limiting spectral distribution of random matrices with unequal variance entriesShaojia Jin0Junshan Xie1School of Mathematics and Statistics, Wuhan UniversitySchool of Mathematics and Statistics, Henan UniversityAbstract A classical result in random matrix theory reveals that the limiting spectral distribution of a Wigner matrix whose entries have a common variance and satisfy other regular assumptions almost surely converges to the semicircular law. In the paper, we will relax the assumption of uniform covariance of each entry, when the average of the normalized sums of the variances in each row of the data matrix converges to a constant, we prove that the same limiting spectral distribution holds. A similar result on a sample covariance matrix is also established. The proofs mainly depend on the Stein equation and the generalized Stein equation of independent random variables.http://link.springer.com/article/10.1186/s13660-020-02440-7Limiting spectral distributionUnequal varianceStein equation |
| spellingShingle | Shaojia Jin Junshan Xie A result on the limiting spectral distribution of random matrices with unequal variance entries Journal of Inequalities and Applications Limiting spectral distribution Unequal variance Stein equation |
| title | A result on the limiting spectral distribution of random matrices with unequal variance entries |
| title_full | A result on the limiting spectral distribution of random matrices with unequal variance entries |
| title_fullStr | A result on the limiting spectral distribution of random matrices with unequal variance entries |
| title_full_unstemmed | A result on the limiting spectral distribution of random matrices with unequal variance entries |
| title_short | A result on the limiting spectral distribution of random matrices with unequal variance entries |
| title_sort | result on the limiting spectral distribution of random matrices with unequal variance entries |
| topic | Limiting spectral distribution Unequal variance Stein equation |
| url | http://link.springer.com/article/10.1186/s13660-020-02440-7 |
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