Recent results of quantum ergodicity on graphs and further investigation

Anantharaman, Nalini; Sabri, Mostafa

Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Volume spécial en l’honneur de Jean-Pierre OTAL “Low dimensional topology, hyperbolic manifolds and spectral geometry”, Tome 28 (2019) no. 3, pp. 559-592.

Nous décrivons des résultats récents d’ergodicité quantique sur les grands graphes, et donnons de nouveaux exemples d’applications à des graphes non-réguliers. Nous mentionnons aussi plusieurs questions ouvertes.

We outline some recent proofs of quantum ergodicity on large graphs and give new applications in the context of irregular graphs. We also discuss some remaining questions.

Classification : 82B44, 58J5147B80, 60B20
Mots-clés : Quantum ergodicity, large graphs, delocalization, Anderson model, trees of finite cone type.

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