## Abstract

We prove that the integrated density of states (IDS) of random Schrödinger operators with Anderson-type potentials on L ^{2}(ℝ^{d})for d ≥ 1 is locally Hölder continuous at all energies with the same Hölder exponent 0 < α ≤ 1 as the conditional probability measure for the single-site random variable. As a special case, we prove that if the probability distribution is absolutely continuous with respect to Lebesgue measure with a bounded density, then the IDS is Lipschitz continuous at all energies. The single-site potential u ∈ L_{0}^{∞}(ℝ^{d}) must be nonnegative and compactly supported. The unperturbed Hamiltonian must be periodic and satisfy a unique continuation principle (UCP). We also prove analogous continuity results for the IDS of random Anderson-type perturbations of the Landau Hamiltonian in two dimensions. All of these results follow from a new Wegner estimate for local random Hamiltonians with rather general probability measures.

Original language | English |
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Pages (from-to) | 469-498 |

Number of pages | 30 |

Journal | Duke Mathematical Journal |

Volume | 140 |

Issue number | 3 |

DOIs | |

State | Published - Dec 1 2007 |

## ASJC Scopus subject areas

- Mathematics (all)