no. 4
Super-expanders and warped cones
[Superexpanseurs et cônes tordus]
Sawicki, Damian1
1 Institute of Mathematics Polish Academy of Sciences Śniadeckich 8 00-656 Warszawa (Poland)
Annales de l'Institut Fourier, Tome 70 (2020) no. 4, pp. 1753-1774.

Pour un espace de Banach X, on montre que toute famille de graphes, quasi-isométriques à des niveaux d’un cône tordu 𝒪 Γ Y, est un expanseur relativement à X, si et seulement si la Γ-représentation induite sur L 2 (Y;X) a un trou spectral. Ceci fournit des examples de graphes qui sont un expanseur relativement à tous les espaces de Banach de type non trivial.

For a Banach space X, we show that any family of graphs quasi-isometric to levels of a warped cone 𝒪 Γ Y is an expander with respect to X if and only if the induced Γ-representation on L 2 (Y;X) has a spectral gap. This provides examples of graphs that are an expander with respect to all Banach spaces of non-trivial type.

Reçu le :
Révisé le :
Accepté le :
Publié le :
DOI : 10.5802/aif.3373
Classification : 46B85, 05C25, 37A30, 37C85
Keywords: expander graph, spectral gap, warped cone, quasi-isometry, Rademacher type.
Mot clés : graphe expanseur, trou spectral, cône tordu, quasi-isométrie, type de Rademacher.
Sawicki, Damian 1

1 Institute of Mathematics Polish Academy of Sciences Śniadeckich 8 00-656 Warszawa (Poland)
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Sawicki, Damian. Super-expanders and warped cones. Annales de l'Institut Fourier, Tome 70 (2020) no. 4, pp. 1753-1774. doi : 10.5802/aif.3373. https://aif.centre-mersenne.org/articles/10.5802/aif.3373/

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