Recent results of quantum ergodicity on graphs and further investigation
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 28 (2019) no. 3, pp. 559-592.

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.

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.

Published online:
DOI: 10.5802/afst.1609
Classification: 82B44, 58J5147B80, 60B20
Keywords: Quantum ergodicity, large graphs, delocalization, Anderson model, trees of finite cone type.

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.
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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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, Serie 6, Volume 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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