Daniel Sánchez-Mendoza
Published 2022-03-02Version 1
We state a precise formulation of a conjecture concerning the product of the principal eigenvalue and the sup-norm of the landscape function of the Anderson model restricted to a large box. We first provide the asymptotic of the principal eigenvalue as the size of the box grows and then use it to give a partial proof of the conjecture. For a special case in one dimension we give a complete proof.
Comments: 17 pages, 2 figures
On fluctuations and localization length for the Anderson model on a strip
Counting eigenvalues of Schrödinger operators using the landscape function
GOE statistics for Anderson models on antitrees and thin boxes in $\mathbb{Z}^3$ with deformed Laplacian
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