Recent results of quantum ergodicity on graphs and further investigation
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, 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.

Publié le :
DOI : 10.5802/afst.1609
Classification : 82B44, 58J5147B80, 60B20
Mots clés : Quantum ergodicity, large graphs, delocalization, Anderson model, trees of finite cone type.
Anantharaman, Nalini 1 ; Sabri, Mostafa 2

1 Université de Strasbourg, CNRS, IRMA UMR 7501, F-67000 Strasbourg, France.
2 Department of Mathematics, Faculty of Science, Cairo University, Cairo 12613, Egypt and Université Paris Sud XI, UMR 8628 du CNRS, Laboratoire de Mathématique, Bât. 307, 91405 Orsay Cedex, France.
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Anantharaman, Nalini; Sabri, Mostafa. Recent results of quantum ergodicity on graphs and further investigation. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 28 (2019) no. 3, pp. 559-592. doi : 10.5802/afst.1609. http://www.numdam.org/articles/10.5802/afst.1609/

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