Recent results of quantum ergodicity on graphs and further investigation

Nalini Anantharaman; Mostafa Sabri

doi:10.5802/afst.1609

Nalini Anantharaman ¹ ; Mostafa Sabri 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.

Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 28 (2019) no. 3, pp. 559-592.

Résumé
Abstract

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 : 2019-12-06

Zbl

DOI : 10.5802/afst.1609

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

Affiliations des auteurs :

Nalini Anantharaman ¹ ; Mostafa Sabri ²

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
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Nalini Anantharaman; Mostafa Sabri. 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. https://afst.centre-mersenne.org/articles/10.5802/afst.1609/

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