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Recent results of quantum ergodicity on graphs and further investigation
Nalini Anantharaman; Mostafa Sabri
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 28 (2019) no. 3, p. 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 : 2019-12-06
DOI : https://doi.org/10.5802/afst.1609
Classification:  82B44,  58J5147B80,  60B20
Keywords: Quantum ergodicity, large graphs, delocalization, Anderson model, trees of finite cone type.
@article{AFST_2019_6_28_3_559_0,
     author = {Nalini Anantharaman and Mostafa Sabri},
     title = {Recent results of quantum ergodicity on graphs and further investigation},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {Ser. 6, 28},
     number = {3},
     year = {2019},
     pages = {559-592},
     doi = {10.5802/afst.1609},
     language = {en},
     url = {https://afst.centre-mersenne.org/item/AFST_2019_6_28_3_559_0}
}
Anantharaman, Nalini; Sabri, Mostafa. 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/item/AFST_2019_6_28_3_559_0/

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