Cogrowth and spectral gap of generic groups
[Cocroissance et trou spectral des groupes génériques]
Ollivier, Yann1
1 UMPA - CNRS, École normale supérieure de Lyon, 46 allée d'Italie, 69364 Lyon Cedex 07 (France)
Annales de l'Institut Fourier, Tome 55 (2005) no. 1, pp. 289-317.

L'exposant de cocroissance d'un groupe contrôle le spectre de la marche aléatoire. Nous prouvons que pour un groupe générique (dans le modèle à densité) cet exposant est arbitrairement proche de celui du groupe libre. En outre, cet exposant est stable par quotient aléatoire d'un groupe hyperbolique sans torsion.

The cogrowth exponent of a group controls the random walk spectrum. We prove that for a generic group (in the density model) this exponent is arbitrarily close to that of a free group. Moreover, this exponent is stable under random quotients of torsion-free hyperbolic groups.

DOI : 10.5802/aif.2099
Classification : 20P05, 20F69, 20F06
Keywords: Random groups, cogrowth, hyperbolic groups, random walk on groups
Mot clés : groupes aléatoires, cocroissance, groupes hyperboliques, marche aléatoire sur les groupes
Ollivier, Yann 1

1 UMPA - CNRS, École normale supérieure de Lyon, 46 allée d'Italie, 69364 Lyon Cedex 07 (France) 
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Ollivier, Yann. Cogrowth and spectral gap of generic groups. Annales de l'Institut Fourier, Tome 55 (2005) no. 1, pp. 289-317. doi : 10.5802/aif.2099. https://www.numdam.org/articles/10.5802/aif.2099/

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