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Eigenvalue Curves of Asymmetric Tridiagonal Matrices

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Eigenvalue Curves of Asymmetric Tridiagonal Matrices
2.	Creator	Author's name, affiliation, country	Ilya Ya Goldsheid; University of London
2.	Creator	Author's name, affiliation, country	Boris A Khoruzhenko; University of London
3.	Subject	Discipline(s)	Mathematics
3.	Subject	Keyword(s)	Random matrix, Schrödinger operator, Lyapunov exponent, eigenvalue distribution, complex eigenvalue.
3.	Subject	Subject classification	82B44, 47B36, 15A52, 47B80, 47B39, 60H25, 37H15
4.	Description	Abstract	Random Schrödinger operators with imaginary vector potentials are studied in dimension one. These operators are non-Hermitian and their spectra lie in the complex plane. We consider the eigenvalue problem on finite intervals of length $n$ with periodic boundary conditions and describe the limit eigenvalue distribution when $n$ goes to infinity. We prove that this limit distribution is supported by curves in the complex plane. We also obtain equations for these curves and for the corresponding eigenvalue density in terms of the Lyapunov exponent and the integrated density of states of a "reference" symmetric eigenvalue problem. In contrast to these results, the spectrum of the limit operator in $\ell^2(Z)$ is a two dimensional set which is not approximated by the spectra of the finite-interval operators.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	2000-11-21
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ejp.ejpecp.org/article/view/72
10.	Identifier	Digital Object Identifier	10.1214/EJP.v5-72
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 5
12.	Language	English=en	en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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