The Wegner estimate and the integrated density of states for some random operators

DOI10.1007/BF02829639zbMath1009.47060OpenAlexW1987763515MaRDI QIDQ1599739

Frédéric Klopp, Shu Nakamura, Peter D. Hislop, Jean-Michel Combes

Publication date: 15 April 2003

Published in: Proceedings of the Indian Academy of Sciences. Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02829639

zbMATH Keywords

Schrödinger operatorintegrated density of stateslocalizationrandom potentialslocal Hölder continuityrandom systemtrace ideal\(L^p\)-theory of the spectral shift functionsdeterministic background operatorsunperturbed spectral gap

Mathematics Subject Classification ID

Applications of operator theory in the physical sciences (47N50) Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics (82B44) Waves and radiation in optics and electromagnetic theory (78A40) Random nonlinear operators (47H40)

Related Items (13)

A characterization of the Anderson metal-insulator transport transition ⋮ Level spacing for non-monotone Anderson models ⋮ Wegner estimates and localization for Gaussian random potentials ⋮ $\mathbf {\operatorname {SL} _2({\mathbb {R}})}$, exponential Herglotz representations, and spectral averaging ⋮ A comprehensive proof of localization for continuous Anderson models with singular random potentials ⋮ Wegner estimates for sign-changing single site potentials ⋮ Some abstract Wegner estimates with applications ⋮ Continuity of integrated density of states -- independent randomness ⋮ Weak convergence of spectral shift functions for one‐dimensional Schrödinger operators ⋮ Wegner estimate and localization for random magnetic fields ⋮ Spectral analysis of percolation Hamiltonians ⋮ Wegner estimate for sparse and other generalized alloy type potentials ⋮ Anderson localization and Lifshits tails for random surface potentials

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