Eigenvector statistics in non-Hermitian random matrix ensembles
We study statistical properties of the eigenvectors of non-Hermitian random matrices, concentrating on Ginibre's complex Gaussian ensemble, in which the real and imaginary parts of each element of an N x N matrix, J, are independent random variables. Calculating ensemble averages based on the q...
| Main Authors: | , |
|---|---|
| Format: | Journal article |
| Language: | English |
| Published: |
1998
|
| _version_ | 1797080074734796800 |
|---|---|
| author | Chalker, J Mehlig, B |
| author_facet | Chalker, J Mehlig, B |
| author_sort | Chalker, J |
| collection | OXFORD |
| description | We study statistical properties of the eigenvectors of non-Hermitian random matrices, concentrating on Ginibre's complex Gaussian ensemble, in which the real and imaginary parts of each element of an N x N matrix, J, are independent random variables. Calculating ensemble averages based on the quantity $< L_\alpha | L_\beta > < R_\beta | R_\alpha >$, where $< L_\alpha |$ and $| R_\beta >$ are left and right eigenvectors of J, we show for large N that eigenvectors associated with a pair of eigenvalues are highly correlated if the two eigenvalues lie close in the complex plane. We examine consequences of these correlations that are likely to be important in physical applications. |
| first_indexed | 2024-03-07T00:54:57Z |
| format | Journal article |
| id | oxford-uuid:87b988f6-1855-4b26-8c33-966c95d29768 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T00:54:57Z |
| publishDate | 1998 |
| record_format | dspace |
| spelling | oxford-uuid:87b988f6-1855-4b26-8c33-966c95d297682022-03-26T22:12:29ZEigenvector statistics in non-Hermitian random matrix ensemblesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:87b988f6-1855-4b26-8c33-966c95d29768EnglishSymplectic Elements at Oxford1998Chalker, JMehlig, BWe study statistical properties of the eigenvectors of non-Hermitian random matrices, concentrating on Ginibre's complex Gaussian ensemble, in which the real and imaginary parts of each element of an N x N matrix, J, are independent random variables. Calculating ensemble averages based on the quantity $< L_\alpha | L_\beta > < R_\beta | R_\alpha >$, where $< L_\alpha |$ and $| R_\beta >$ are left and right eigenvectors of J, we show for large N that eigenvectors associated with a pair of eigenvalues are highly correlated if the two eigenvalues lie close in the complex plane. We examine consequences of these correlations that are likely to be important in physical applications. |
| spellingShingle | Chalker, J Mehlig, B Eigenvector statistics in non-Hermitian random matrix ensembles |
| title | Eigenvector statistics in non-Hermitian random matrix ensembles |
| title_full | Eigenvector statistics in non-Hermitian random matrix ensembles |
| title_fullStr | Eigenvector statistics in non-Hermitian random matrix ensembles |
| title_full_unstemmed | Eigenvector statistics in non-Hermitian random matrix ensembles |
| title_short | Eigenvector statistics in non-Hermitian random matrix ensembles |
| title_sort | eigenvector statistics in non hermitian random matrix ensembles |
| work_keys_str_mv | AT chalkerj eigenvectorstatisticsinnonhermitianrandommatrixensembles AT mehligb eigenvectorstatisticsinnonhermitianrandommatrixensembles |