H�lder Equicontinuity of the Integrated Density of States at Weak Disorder

2004/03/31 by Jeffrey Schenker, Jeffrey H Schenker
Mathematics · Physics and Astronomy · #Quantum chaos and dynamical systems #Random Matrices and Applications #Spectral Theory in Mathematical Physics #math-ph #math.MP

paper · pdf · doi:10.1007/s11005-004-3757-x

published as Lett. Math. Phys. 70 (2004), 195-209. · 15 Pages, typos corrected, comments and ref. [1] added, theorems 3,4 combined

arxiv created 2004/08/16 · openalex publication_date 2004/12/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/29

Abstract

Hölder continuity, |N_λ(E)-N_λ(E')|≤ C |E-E'|^α, with a constant C independent of the disorder strength λ is proved for the integrated density of states N_λ(E) associated to a discrete random operator H = H_o + λV consisting of a translation invariant hopping matrix H_o and i.i.d. single site potentials V with an absolutely continuous distribution, under a regularity assumption for the hopping term.

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