# Hölder Continuity of the Integrated Density of States in the One-Dimensional Anderson Model

Hölder Continuity of the Integrated Density of States in the One-Dimensional Anderson Model We consider the one-dimensional random Schrödinger operator $$H_{\omega} = H_0 + \sigma V_{\omega},$$ H ω = H 0 + σ V ω , where the potential V has i.i.d. entries with bounded support. We prove that the IDS is Hölder continuous with exponent $${1-c \sigma}$$ 1 - c σ . This improves upon the work of Bourgain showing that the Hölder exponent tends to 1 as sigma tends to 0 in the more specific Anderson–Bernoulli setting. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Communications in Mathematical Physics Springer Journals

# Hölder Continuity of the Integrated Density of States in the One-Dimensional Anderson Model

, Volume 355 (3) – Jul 7, 2017
25 pages

/lp/springer_journal/h-lder-continuity-of-the-integrated-density-of-states-in-the-one-59XWjvKgx0
Publisher
Springer Berlin Heidelberg
Subject
Physics; Theoretical, Mathematical and Computational Physics; Mathematical Physics; Quantum Physics; Complex Systems; Classical and Quantum Gravitation, Relativity Theory
ISSN
0010-3616
eISSN
1432-0916
D.O.I.
10.1007/s00220-017-2927-5
Publisher site
See Article on Publisher Site

## You’re reading a free preview. Subscribe to read the entire article.

### DeepDyve is your personal research library

It’s your single place to instantly
that matters to you.

over 12 million articles from more than
10,000 peer-reviewed journals.

All for just $49/month ### Explore the DeepDyve Library ### Unlimited reading Read as many articles as you need. Full articles with original layout, charts and figures. Read online, from anywhere. ### Stay up to date Keep up with your field with Personalized Recommendations and Follow Journals to get automatic updates. ### Organize your research It’s easy to organize your research with our built-in tools. ### Your journals are on DeepDyve Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more. All the latest content is available, no embargo periods. ### Monthly Plan • Read unlimited articles • Personalized recommendations • No expiration • Print 20 pages per month • 20% off on PDF purchases • Organize your research • Get updates on your journals and topic searches$49/month

14-day Free Trial

Best Deal — 39% off

### Annual Plan

• All the features of the Professional Plan, but for 39% off!
• Billed annually
• No expiration
• For the normal price of 10 articles elsewhere, you get one full year of unlimited access to articles.

$588$360/year

billed annually

14-day Free Trial