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

Etienne Le Masson (1, 2) , Mostafa Sabri (3)

1 UCP - Université de Cergy Pontoise
2 AGM - UMR 8088 - Analyse, Géométrie et Modélisation
3 LM-Orsay - Laboratoire de Mathématiques d'Orsay

This article is concerned with properties of delocalization for eigenfunctions of Schrödinger operators on large finite graphs. More specifically, we provide $L^p$-norm estimates for such eigenfunctions and show that they have a large support. Our estimates hold for any fixed, possibly irregular graph, in prescribed energy regions, and also for certain sequences of graphs such as N-lifts.

Domaines: Théorie spectrale [math.SP]; Physique mathématique [math-ph]

Etienne Le Masson, Mostafa Sabri. $L^p$ norms and support of eigenfunctions on graphs. Comm. Math. Phys, 2020, 374, pp.211-240. ⟨10.1007/s00220-019-03473-w⟩. ⟨hal-01875505⟩