$L^p$ norms and support of eigenfunctions on graphs

Abstract

This article is concerned with properties of delocalization for eigenfunctions of Schrödinger operators on large finite graphs. More specifically, we show that the eigenfunctions have a large support and we assess their lp-norms. Our estimates hold for any fixed, possibly irregular graph, in prescribed energy regions, and also for certain sequences of graphs such as N-lifts.

To appear in Comm. Math. Phys

References in corpus (2)

• Level compressibility for the Anderson model on regular random graphs and the eigenvalue statistics in the extended phase
• Quantum ergodicity for the Anderson model on regular graphs

Cited by in corpus (1)

• Sturm-Liouville Problems And Global Bounds By Small Control Sets And applications to quantum graphs