Geodesic
Kazhdan Constants of Hyperbolic Groups
Funkcionalʹnyj analiz i ego priloženiâ, Tome 36 (2002) no. 4, pp. 46-54

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Let $H$ be an infinite hyperbolic group with Kazhdan property $(T)$ and let $\varkappa(H,X)$ denote the Kazhdan constant of $H$ with respect to a generating set $X$. We prove that $\inf_{X}\varkappa(H,X)=0$, where the infimum is taken over all finite generating sets of $H$. In particular, this gives an answer to a Lubotzky question.
Keywords: Kazhdan property (T), hyperbolic group, left regular representation
Mots-clés : amenable group. 
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     author = {D. V. Osin},
     title = {Kazhdan {Constants} of {Hyperbolic} {Groups}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {46--54},
     publisher = {mathdoc},
     volume = {36},
     number = {4},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2002_36_4_a3/}
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D. V. Osin. Kazhdan Constants of Hyperbolic Groups. Funkcionalʹnyj analiz i ego priloženiâ, Tome 36 (2002) no. 4, pp. 46-54. http://geodesic.mathdoc.fr/item/FAA_2002_36_4_a3/