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.
Classification : 20P05, 20F69, 20F06
Mots clés : groupes aléatoires, cocroissance, groupes hyperboliques, marche aléatoire sur les groupes
@article{AIF_2005__55_1_289_0, author = {Ollivier, Yann}, title = {Cogrowth and spectral gap of generic groups}, journal = {Annales de l'Institut Fourier}, pages = {289--317}, publisher = {Association des Annales de l'institut Fourier}, volume = {55}, number = {1}, year = {2005}, doi = {10.5802/aif.2099}, zbl = {02162474}, mrnumber = {2141699}, language = {en}, url = {archive.numdam.org/item/AIF_2005__55_1_289_0/} }
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. http://archive.numdam.org/item/AIF_2005__55_1_289_0/
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