Limiting behavior of eigenvectors of large Wigner matrices
A new form of empirical spectral distribution of a Wigner matrix Wn with weights specified by the eigenvectors is defined and it is then shown to converge with probability one to the semicircular law. Moreover, central limit theorem for linear spectral statistics defined by the eigenvectors and eige...
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sg-ntu-dr.10356-993222020-03-07T12:37:12Z Limiting behavior of eigenvectors of large Wigner matrices Bai, Z. D. Pan, G. M. School of Physical and Mathematical Sciences DRNTU::Science::Mathematics A new form of empirical spectral distribution of a Wigner matrix Wn with weights specified by the eigenvectors is defined and it is then shown to converge with probability one to the semicircular law. Moreover, central limit theorem for linear spectral statistics defined by the eigenvectors and eigenvalues is also established under some moment conditions, which suggests that the eigenvector matrix of Wn is close to being Haar distributed. 2013-10-31T07:02:15Z 2019-12-06T20:05:54Z 2013-10-31T07:02:15Z 2019-12-06T20:05:54Z 2011 2011 Journal Article Bai, Z. D., & Pan, G. M. (2011). Limiting behavior of eigenvectors of large Wigner matrices. Journal of statistical physics, 146(3), 519-549. https://hdl.handle.net/10356/99322 http://hdl.handle.net/10220/17138 10.1007/s10955-011-0407-4 en Journal of statistical physics |
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DRNTU::Science::Mathematics Bai, Z. D. Pan, G. M. Limiting behavior of eigenvectors of large Wigner matrices |
| description |
A new form of empirical spectral distribution of a Wigner matrix Wn with weights specified by the eigenvectors is defined and it is then shown to converge with probability one to the semicircular law. Moreover, central limit theorem for linear spectral statistics defined by the eigenvectors and eigenvalues is also established under some moment conditions, which suggests that the eigenvector matrix of Wn is close to being Haar distributed. |
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School of Physical and Mathematical Sciences |
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School of Physical and Mathematical Sciences Bai, Z. D. Pan, G. M. |
| format |
Article |
| author |
Bai, Z. D. Pan, G. M. |
| author_sort |
Bai, Z. D. |
| title |
Limiting behavior of eigenvectors of large Wigner matrices |
| title_short |
Limiting behavior of eigenvectors of large Wigner matrices |
| title_full |
Limiting behavior of eigenvectors of large Wigner matrices |
| title_fullStr |
Limiting behavior of eigenvectors of large Wigner matrices |
| title_full_unstemmed |
Limiting behavior of eigenvectors of large Wigner matrices |
| title_sort |
limiting behavior of eigenvectors of large wigner matrices |
| publishDate |
2013 |
| url |
https://hdl.handle.net/10356/99322 http://hdl.handle.net/10220/17138 |
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1681036963055927296 |