Cogrowth and spectral gap of generic groups
Annales de l'Institut Fourier, Volume 55 (2005) no. 1, p. 289-317

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.

DOI : https://doi.org/10.5802/aif.2099
Classification:  20P05,  20F69,  20F06
Keywords: Random groups, cogrowth, hyperbolic groups, random walk on groups 
@article{AIF_2005__55_1_289_0,
     author = {Ollivier, Yann},
     title = {Cogrowth and spectral gap of generic groups},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {55},
     number = {1},
     year = {2005},
     pages = {289-317},
     doi = {10.5802/aif.2099},
     zbl = {02162474},
     mrnumber = {2141699},
     language = {en},
     url = {http://www.numdam.org/item/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://www.numdam.org/item/AIF_2005__55_1_289_0/

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