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.
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.
Keywords: Random groups, cogrowth, hyperbolic groups, random walk on groups
Mot 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{\textquoteright}institut Fourier}, volume = {55}, number = {1}, year = {2005}, doi = {10.5802/aif.2099}, mrnumber = {2141699}, zbl = {02162474}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.2099/} }
TY - JOUR AU - Ollivier, Yann TI - Cogrowth and spectral gap of generic groups JO - Annales de l'Institut Fourier PY - 2005 SP - 289 EP - 317 VL - 55 IS - 1 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.2099/ DO - 10.5802/aif.2099 LA - en ID - AIF_2005__55_1_289_0 ER -
%0 Journal Article %A Ollivier, Yann %T Cogrowth and spectral gap of generic groups %J Annales de l'Institut Fourier %D 2005 %P 289-317 %V 55 %N 1 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.2099/ %R 10.5802/aif.2099 %G en %F AIF_2005__55_1_289_0
Ollivier, Yann. Cogrowth and spectral gap of generic groups. Annales de l'Institut Fourier, Volume 55 (2005) no. 1, pp. 289-317. doi : 10.5802/aif.2099. http://archive.numdam.org/articles/10.5802/aif.2099/
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