Details
| Original language | English |
|---|---|
| Pages (from-to) | 515-533 |
| Number of pages | 19 |
| Journal | Journal of functional analysis |
| Volume | 253 |
| Issue number | 2 |
| Publication status | Published - 15 Dec 2007 |
| Externally published | Yes |
Abstract
We consider ergodic random Schrödinger operators on the metric graph Zd with random potentials and random boundary conditions taking values in a finite set. We show that normalized finite volume eigenvalue counting functions converge to a limit uniformly in the energy variable. This limit, the integrated density of states, can be expressed by a closed Shubin-Pastur type trace formula. It supports the spectrum and its points of discontinuity are characterized by existence of compactly supported eigenfunctions. Among other examples we discuss random magnetic fields and percolation models.
Keywords
- Integrated density of states, Metric graph, Quantum graph, Random Schrödinger operator
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
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In: Journal of functional analysis, Vol. 253, No. 2, 15.12.2007, p. 515-533.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Uniform existence of the integrated density of states for random Schrödinger operators on metric graphs over Zd
AU - Gruber, Michael J.
AU - Lenz, Daniel H.
AU - Veselić, Ivan
N1 - Funding information: It is a pleasure to thank Mario Helm for interesting discussions. The authors were financially supported by the DFG, two of them (M.G. and I.V.) under grant Ve 253/2-2 within the Emmy-Noether-Programme.
PY - 2007/12/15
Y1 - 2007/12/15
N2 - We consider ergodic random Schrödinger operators on the metric graph Zd with random potentials and random boundary conditions taking values in a finite set. We show that normalized finite volume eigenvalue counting functions converge to a limit uniformly in the energy variable. This limit, the integrated density of states, can be expressed by a closed Shubin-Pastur type trace formula. It supports the spectrum and its points of discontinuity are characterized by existence of compactly supported eigenfunctions. Among other examples we discuss random magnetic fields and percolation models.
AB - We consider ergodic random Schrödinger operators on the metric graph Zd with random potentials and random boundary conditions taking values in a finite set. We show that normalized finite volume eigenvalue counting functions converge to a limit uniformly in the energy variable. This limit, the integrated density of states, can be expressed by a closed Shubin-Pastur type trace formula. It supports the spectrum and its points of discontinuity are characterized by existence of compactly supported eigenfunctions. Among other examples we discuss random magnetic fields and percolation models.
KW - Integrated density of states
KW - Metric graph
KW - Quantum graph
KW - Random Schrödinger operator
UR - http://www.scopus.com/inward/record.url?scp=36048954578&partnerID=8YFLogxK
U2 - 10.1016/j.jfa.2007.09.003
DO - 10.1016/j.jfa.2007.09.003
M3 - Article
AN - SCOPUS:36048954578
VL - 253
SP - 515
EP - 533
JO - Journal of functional analysis
JF - Journal of functional analysis
SN - 0022-1236
IS - 2
ER -