For a Banach space , we show that any family of graphs quasi-isometric to levels of a warped cone is an expander with respect to if and only if the induced -representation on 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 , on montre que toute famille de graphes, quasi-isométriques à des niveaux d’un cône tordu , est un expanseur relativement à , si et seulement si la -représentation induite sur 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.
Revised:
Accepted:
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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
@article{AIF_2020__70_4_1753_0, author = {Sawicki, Damian}, title = {Super-expanders and warped cones}, journal = {Annales de l'Institut Fourier}, pages = {1753--1774}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {70}, number = {4}, year = {2020}, doi = {10.5802/aif.3373}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3373/} }
TY - JOUR AU - Sawicki, Damian TI - Super-expanders and warped cones JO - Annales de l'Institut Fourier PY - 2020 SP - 1753 EP - 1774 VL - 70 IS - 4 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.3373/ DO - 10.5802/aif.3373 LA - en ID - AIF_2020__70_4_1753_0 ER -
%0 Journal Article %A Sawicki, Damian %T Super-expanders and warped cones %J Annales de l'Institut Fourier %D 2020 %P 1753-1774 %V 70 %N 4 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.3373/ %R 10.5802/aif.3373 %G en %F AIF_2020__70_4_1753_0
Sawicki, Damian. Super-expanders and warped cones. Annales de l'Institut Fourier, Volume 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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