Illinois Journal of Mathematics

Continuity with respect to disorder of the integrated density of states

Peter D. Hislop, Frédéric Klopp, and Jeffrey H. Schenker

Full-text: Open access

Abstract

We prove that the integrated density of states (IDS) associated to a random Schrödinger operator is locally uniformly Hölder continuous as a function of the disorder parameter $\lambda$. In particular, we obtain convergence of the IDS, as $\lambda \rightarrow 0$, to the IDS for the unperturbed operator at all energies for which the IDS for the unperturbed operator is continuous in energy.

Article information

Source
Illinois J. Math. Volume 49, Number 3 (2005), 893-904.

Dates
First available in Project Euclid: 13 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1258138226

Mathematical Reviews number (MathSciNet)
MR2210266

Zentralblatt MATH identifier
1091.47031

Subjects
Primary: 47B80: Random operators [See also 47H40, 60H25]
Secondary: 34L40: Particular operators (Dirac, one-dimensional Schrödinger, etc.) 35P20: Asymptotic distribution of eigenvalues and eigenfunctions 47B25: Symmetric and selfadjoint operators (unbounded) 47F05: Partial differential operators [See also 35Pxx, 58Jxx] (should also be assigned at least one other classification number in section 47)

Citation

Hislop, Peter D.; Klopp, Frédéric; Schenker, Jeffrey H. Continuity with respect to disorder of the integrated density of states. Illinois J. Math. 49 (2005), no. 3, 893--904. https://projecteuclid.org/euclid.ijm/1258138226


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