Expansion of the almost sure spectrum in the weak disorder regime

Denis Borisov (1, 2) , Francisco Hoecker-Escuti (3) , Ivan Veselić (4)

1 Institute of Mathematics
2 Department of Physics and Mathematics
3 Fakultät für Mathematik
4 Professur Stochastik, TU-Chemnitz

The spectrum of random ergodic Schrödinger-type operators is almost surely a deterministic subset of the real line. The random operator can be considered as a perturbation of a periodic one. As soon as the disorder is switched on via a global coupling constant, the spectrum expands. We estimate how much the spectrum expands at its bottom for operators on $\ell^2(\mathbb Z^d)$.

Mots clés: spectral theory; random Schrödinger operators; Floquet theory; weak disorder; Anderson model

Domaines: Physique mathématique [math-ph]

Denis Borisov, Francisco Hoecker-Escuti, Ivan Veselić. Expansion of the almost sure spectrum in the weak disorder regime. 2014. ⟨hal-01053573⟩