A Note on Random Perturbations of a Multiple Eigenvalue of a Hermitian Operator

G. Gaines, K. Kaphle and F. Ruymgaart ()
Additional contact information
G. Gaines: Texas Tech University
K. Kaphle: University of Maine at Fort Kent
F. Ruymgaart: Texas Tech University

Journal of Theoretical Probability, 2014, vol. 27, issue 4, 1112-1123

Abstract: Abstract 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.

Keywords: Random perturbation; Hermitian operator; Isolated eigenvalue; Multiplicity; Primary: 60H25; Secondary: 47B80 (search for similar items in EconPapers)
Date: 2014
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10959-013-0482-3 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jotpro:v:27:y:2014:i:4:d:10.1007_s10959-013-0482-3

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10959

DOI: 10.1007/s10959-013-0482-3

Access Statistics for this article

Journal of Theoretical Probability is currently edited by Andrea Monica

More articles in Journal of Theoretical Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().