Principal Eigenvalue and Landscape Function of the Anderson Model on a Large Box

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.

18 pages, 2 figures. This version contains an improvement of Theorem 2 and a complete rewrite of Section 3

References in corpus (1)

• Approximating the ground state eigenvalue via the effective potential

Cited by in corpus (1)

• Landscape approximation of the ground state eigenvalue for graphs and random hopping models