Cogrowth and spectral gap of generic groups
| dc.creator | Ollivier, Yann | |
| dc.date | 2004-01-06 | |
| dc.date | 2004-03-18 | |
| dc.date.accessioned | 2026-07-07T05:04:23Z | |
| dc.date.available | 2026-07-07T05:04:23Z | |
| dc.description | We prove that that for all $\eps$, having cogrowth exponent at most $1/2+\eps$ (in base $2m-1$ with $m$ the number of generators) is a generic property of groups in the density model of random groups. This generalizes a theorem of Grigorchuk and Champetier. More generally we show that the cogrowth of a random quotient of a torsion-free hyperbolic group stays close to that of this group. This proves in particular that the spectral gap of a generic group is as large as it can be. | |
| dc.description | 2nd version: full redaction, 24 pages | |
| dc.identifier | https://arxiv.org/abs/math/0401048 | |
| dc.identifier | http://arxiv.org/abs/math/0401048 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69785 | |
| dc.subject | Group Theory | |
| dc.subject | 20P05; 20F69; 20F06 | |
| dc.title | Cogrowth and spectral gap of generic groups | |
| dc.type | text |