Fluctuations of Linear Eigenvalues Statistics for Wigner Matrices: Edge Case
In this note, we consider the fluctuation theorem for X(n)fn := ∑f(λi)I(λi≥θn), where λi, i=1,…,n are eigenvalues from a Wigner matrix and θn→2−. We prove that in the edge case X(n)fn behaves like the counting function of Wigner matrix. Our results can be viewed as a complement of Bao et al. (J Stat...
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sg-ntu-dr.10356-856002023-02-28T19:33:07Z Fluctuations of Linear Eigenvalues Statistics for Wigner Matrices: Edge Case Pan, Guangming Wang, Shaochen Zhou, Wang School of Physical and Mathematical Sciences Wigner matrix Linear eigenvalue statistic In this note, we consider the fluctuation theorem for X(n)fn := ∑f(λi)I(λi≥θn), where λi, i=1,…,n are eigenvalues from a Wigner matrix and θn→2−. We prove that in the edge case X(n)fn behaves like the counting function of Wigner matrix. Our results can be viewed as a complement of Bao et al. (J Stat Phys 150(1):88–129, 2013). MOE (Min. of Education, S’pore) Accepted version 2017-09-18T04:56:42Z 2019-12-06T16:06:54Z 2017-09-18T04:56:42Z 2019-12-06T16:06:54Z 2016 Journal Article Pan, G., Wang, S., & Zhou, W. (2016). Fluctuations of Linear Eigenvalues Statistics for Wigner Matrices: Edge Case. Journal of Statistical Physics, 165(3), 507-520. 0022-4715 https://hdl.handle.net/10356/85600 http://hdl.handle.net/10220/43758 10.1007/s10955-016-1618-5 en Journal of Statistical Physics © 2016 Springer Science+Business Media New York. This is the author created version of a work that has been peer reviewed and accepted for publication by Journal of Statistical Physics, Springer Science+Business Media New York. It incorporates referee’s comments but changes resulting from the publishing process, such as copyediting, structural formatting, may not be reflected in this document. The published version is available at: [http://dx.doi.org/10.1007/s10955-016-1618-5]. 14 p. application/pdf |
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Wigner matrix Linear eigenvalue statistic |
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Wigner matrix Linear eigenvalue statistic Pan, Guangming Wang, Shaochen Zhou, Wang Fluctuations of Linear Eigenvalues Statistics for Wigner Matrices: Edge Case |
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In this note, we consider the fluctuation theorem for X(n)fn := ∑f(λi)I(λi≥θn), where λi, i=1,…,n are eigenvalues from a Wigner matrix and θn→2−. We prove that in the edge case X(n)fn behaves like the counting function of Wigner matrix. Our results can be viewed as a complement of Bao et al. (J Stat Phys 150(1):88–129, 2013). |
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School of Physical and Mathematical Sciences |
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School of Physical and Mathematical Sciences Pan, Guangming Wang, Shaochen Zhou, Wang |
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Article |
| author |
Pan, Guangming Wang, Shaochen Zhou, Wang |
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Pan, Guangming |
| title |
Fluctuations of Linear Eigenvalues Statistics for Wigner Matrices: Edge Case |
| title_short |
Fluctuations of Linear Eigenvalues Statistics for Wigner Matrices: Edge Case |
| title_full |
Fluctuations of Linear Eigenvalues Statistics for Wigner Matrices: Edge Case |
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Fluctuations of Linear Eigenvalues Statistics for Wigner Matrices: Edge Case |
| title_full_unstemmed |
Fluctuations of Linear Eigenvalues Statistics for Wigner Matrices: Edge Case |
| title_sort |
fluctuations of linear eigenvalues statistics for wigner matrices: edge case |
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2017 |
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https://hdl.handle.net/10356/85600 http://hdl.handle.net/10220/43758 |
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