A Note on Random Perturbations of a Multiple Eigenvalue of a Hermitian Operator
| Autor: | K. Kaphle, G. Gaines, Frits H. Ruymgaart |
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| Rok vydání: | 2013 |
| Předmět: |
Statistics and Probability
Momentum operator General Mathematics Mathematical analysis Position operator Displacement operator Mathematics::Spectral Theory Hermitian matrix Ladder operator Applied mathematics Statistics Probability and Uncertainty Divide-and-conquer eigenvalue algorithm Eigenvalues and eigenvectors Eigenvalue perturbation Mathematics |
| Zdroj: | Journal of Theoretical Probability. 27:1112-1123 |
| ISSN: | 1572-9230 0894-9840 |
| DOI: | 10.1007/s10959-013-0482-3 |
| Popis: | The problem of a random Hermitian perturbation of a multiple isolated eigenvalue of a Hermitian operator is considered. It is shown that the combined multiplicities of the perturbed eigenvalues converge in probability to the multiplicity of the eigenvalue of the target operator. Also the asymptotic distribution of a certain average of these eigenvalues, centered at the target, is obtained. As a tool differentiation of analytic functions of operators is employed in conjunction with an ensuing “delta-method”. The result is of a probabilistic rather than statistical nature. |
| Databáze: | OpenAIRE |
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