Principal Eigenvalue and Landscape Function of the Anderson Model on a Large Box
Mathematical Physics
2025-03-24 v2 math.MP
Spectral Theory
Abstract
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. We give a complete proof for the one dimensional case.
Cite
@article{arxiv.2203.01059,
title = {Principal Eigenvalue and Landscape Function of the Anderson Model on a Large Box},
author = {Daniel Sánchez-Mendoza},
journal= {arXiv preprint arXiv:2203.01059},
year = {2025}
}
Comments
18 pages, 2 figures. This version contains an improvement of Theorem 2 and a complete rewrite of Section 3