Continuity with respect to disorder of the integrated density of states

Peter D. Hislop; Frédéric Klopp; Jeffrey H. Schenker

doi:10.1215/ijm/1258138226

Continuity with respect to disorder of the integrated density of states

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

Mathematics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

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 λ. In particular, we obtain convergence of the IDS, as λ → 0, to the IDS for the unperturbed operator at all energies for which the IDS for the unperturbed operator is continuous in energy.

Original language	English
Pages (from-to)	893-904
Number of pages	12
Journal	Illinois Journal of Mathematics
Volume	49
Issue number	3
DOIs	https://doi.org/10.1215/ijm/1258138226
State	Published - 2005

ASJC Scopus subject areas

Mathematics (all)

Access to Document

10.1215/ijm/1258138226

Cite this

@article{f7c8cab2087e4a6fb1e91067bef2fa58,

title = "Continuity with respect to disorder of the integrated density of states",

abstract = "We prove that the integrated density of states (IDS) associated to a random Schr{\"o}dinger operator is locally uniformly H{\"o}lder continuous as a function of the disorder parameter λ. In particular, we obtain convergence of the IDS, as λ → 0, to the IDS for the unperturbed operator at all energies for which the IDS for the unperturbed operator is continuous in energy.",

author = "Hislop, {Peter D.} and Fr{\'e}d{\'e}ric Klopp and Schenker, {Jeffrey H.}",

year = "2005",

doi = "10.1215/ijm/1258138226",

language = "English",

volume = "49",

pages = "893--904",

number = "3",

}

TY - JOUR

T1 - Continuity with respect to disorder of the integrated density of states

AU - Hislop, Peter D.

AU - Klopp, Frédéric

AU - Schenker, Jeffrey H.

PY - 2005

Y1 - 2005

N2 - 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 λ. In particular, we obtain convergence of the IDS, as λ → 0, to the IDS for the unperturbed operator at all energies for which the IDS for the unperturbed operator is continuous in energy.

AB - 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 λ. In particular, we obtain convergence of the IDS, as λ → 0, to the IDS for the unperturbed operator at all energies for which the IDS for the unperturbed operator is continuous in energy.

UR - http://www.scopus.com/inward/record.url?scp=33745644487&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33745644487&partnerID=8YFLogxK

U2 - 10.1215/ijm/1258138226

DO - 10.1215/ijm/1258138226

M3 - Article

AN - SCOPUS:33745644487

VL - 49

SP - 893

EP - 904

IS - 3

ER -

Continuity with respect to disorder of the integrated density of states

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this