## Abstract

We prove that the integrated density of states (IDS) for the randomly perturbed Landau Hamiltonian is Hölder continuous at all energies with any Hölder exponent < q < 1. The random Anderson-type potential is constructed with a non-negative, compactly supported single-site potential u. The distribution of the iid random variables is required to be absolutely continuous with a bounded, compactly upported density. This extends a previous result Combes et al. [Combes, J. M., Hislop, P. D., Klopp, F. (2003a). Hölder continuity of the integrated density of states for some random operators at all energies. Int. Math. Res. Notices 2003: 179-209] that was restricted to constant magnetic fields having rational flux through the unit square. We also prove that the IDS is Hölder continuous as a function of the nonzero magnetic field strength.

Original language | English |
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Pages (from-to) | 1187-1213 |

Number of pages | 27 |

Journal | Communications in Partial Differential Equations |

Volume | 29 |

Issue number | 7-8 |

DOIs | |

State | Published - Jul 2004 |

### Bibliographical note

Funding Information:The first author is supported by CPT, CNRS, Luminy, Marseille, France; the second author is supported in part by NSF Grant DMS-0202656; the third author is supported in part by FNS 2000 ‘‘Programme Jeunes Chercheurs’’, and by the Chilean Science Foundation Fondecyt under Grant 7020737; the fourth author is Supported in part by Chilean Science Foundation Fondecyt under Grants 1020737 and 7020737.

## Keywords

- Irrational flux
- Landau levels
- Localization
- Magnetic fields
- Random Schrödinger operators

## ASJC Scopus subject areas

- Analysis
- Applied Mathematics