The landscape law for tight binding Hamiltonians

Abstract

The present paper extends the landscape theory pioneered in [FM, ADFJM2, DFM] to the tight-binding Schrödinger operator on ${\mathbb{Z}}^d$. In particular, we establish upper and lower bounds for the integrated density of states in terms of the counting function based upon the localization landscape.

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Cited by in corpus (2)

• Applications of the landscape function for Schrödinger operators with singular potentials and irregular magnetic fields
• Landscape approximation of the ground state eigenvalue for graphs and random hopping models