Super-expanders and warped cones

Sawicki, Damian

doi:10.5802/aif.3373

Geodesic

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Super-expanders and warped cones
[Superexpanseurs et cônes tordus]

Sawicki, Damian ¹

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.

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Abstract (VO)
Résumé

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.

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.

Reçu le : 2018-06-11
Révisé le : 2019-06-03
Accepté le : 2019-07-11
Publié le : 2021-04-15

DOI : 10.5802/aif.3373

Classification : 46B85, 05C25, 37A30, 37C85
Keywords: expander graph, spectral gap, warped cone, quasi-isometry, Rademacher type.
Mots-clés : graphe expanseur, trou spectral, cône tordu, quasi-isométrie, type de Rademacher.

Affiliations des auteurs :

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. http://geodesic.mathdoc.fr/articles/10.5802/aif.3373/

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