Approximating spectral invariants of Harper operators on graphs II

DOI10.1090/S0002-9939-02-06739-4zbMath1045.47028arXivmath/0201127OpenAlexW3101035159MaRDI QIDQ4794593

Varghese Mathai, Thomas Schick, Stuart G. Yates

Publication date: 19 February 2003

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0201127

zbMATH Keywords

integrated density of statesgraphsvon Neumann algebrasamenable groupsapproximation theoremsHarper operatordiscrete magnetic Laplacian (DML)

Mathematics Subject Classification ID

Related Items (13)

A Feynman-Kac-Itô formula for magnetic Schrödinger operators on graphs ⋮ Continuity of the integrated density of states on random length metric graphs ⋮ Arithmetic properties of eigenvalues of generalized Harper operators on graphs ⋮ Uniform existence of the integrated density of states on metric Cayley graphs ⋮ Uniform approximation of the integrated density of states for long-range percolation Hamiltonians ⋮ Uniform existence of the integrated density of states for randomly weighted Hamiltonians on long-range percolation graphs ⋮ A Banach space-valued ergodic theorem and the uniform approximation of the integrated density of states ⋮ Spectral gaps and discrete magnetic Laplacians ⋮ Semiclassical limits of quantum partition functions on infinite graphs ⋮ Spectral analysis of percolation Hamiltonians ⋮ Groupoids, von Neumann algebras and the integrated density of states ⋮ Hamiltonians on discrete structures: jumps of the integrated density of states and uniform convergence ⋮ Approximation of the integrated density of states on sofic groups

Cites Work

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• Approximating \(\ell_2\)-Betti numbers of an amenable covering by ordinary Betti numbers
• Discrete magnetic Laplacian
• Approximating spectral invariants of Harper operators on graphs
• A note on the Følner condition for amenability
• ON THE ANALYTIC ZERO DIVISOR CONJECTURE OF LINNELL
• Approximating L²‐invariants and the Atiyah conjecture

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