Kazhdan Constants for $SL_n(Z)$
| dc.creator | Kassabov, Martin | |
| dc.date | 2003-11-26 | |
| dc.date.accessioned | 2026-07-07T05:03:19Z | |
| dc.date.available | 2026-07-07T05:03:19Z | |
| dc.description | In this article we improve the known Kazhdan constant for $SL_n(Z)$ with respect to the generating set of the elementary matrices. We prove that the Kazhdan constant is bounded from below by $[42\sqrt{n}+860]^{-1}$, which gives the exact asymptotic behavior of the Kazhdan constant, as $n$ goes to infinity, since $\sqrt{2/n}$ is an upper bound. We can use this bound to improve the bounds for the spectral gap of the Cayley graph of $SL_n(F_p)$ and for the working time of the product replacement algorithm for abelian groups. | |
| dc.description | 22 pages | |
| dc.identifier | https://arxiv.org/abs/math/0311487 | |
| dc.identifier | http://arxiv.org/abs/math/0311487 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69365 | |
| dc.subject | Group Theory | |
| dc.subject | Combinatorics | |
| dc.subject | Representation Theory | |
| dc.subject | 20E46 (Primary) 15A36, 22E40, 22E67 (Secondary) | |
| dc.title | Kazhdan Constants for $SL_n(Z)$ | |
| dc.type | text |