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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Main Authors: Bai, Z. D., Pan, G. M.
Other Authors: School of Physical and Mathematical Sciences
Format: Article
Language:English
Published: 2013
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Online Access:https://hdl.handle.net/10356/99322
http://hdl.handle.net/10220/17138
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Institution: Nanyang Technological University
Language: English
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spelling 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
institution Nanyang Technological University
building NTU Library
country Singapore
collection DR-NTU
language English
topic DRNTU::Science::Mathematics
spellingShingle 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.
author2 School of Physical and Mathematical Sciences
author_facet 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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