Comptes Rendus
Group Theory
Spectral gaps in SU(d)
Comptes Rendus. Mathématique, Volume 348 (2010) no. 11-12, pp. 609-611.

It is shown that if g1,,gk are algebraic elements in SU(d) generating a dense subgroup, then the corresponding Hecke operator has a spectral gap.

On démontre que si g1,,gk sont des éléments algébriques de SU(d) et le groupe engendré par g1,,gk est dense, alors l'opérateur de Hecke défini par ces éléments a un trou spectral.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2010.04.024
Jean Bourgain 1; Alexander Gamburd 2

1 IAS, 1 Einstein Drive, Princeton, NJ 08540, USA
2 UCSC, 1156 High Street, Santa Cruz, CA 95064, USA
@article{CRMATH_2010__348_11-12_609_0,
     author = {Jean Bourgain and Alexander Gamburd},
     title = {Spectral gaps in $ \mathit{SU}(d)$},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {609--611},
     publisher = {Elsevier},
     volume = {348},
     number = {11-12},
     year = {2010},
     doi = {10.1016/j.crma.2010.04.024},
     language = {en},
}
TY  - JOUR
AU  - Jean Bourgain
AU  - Alexander Gamburd
TI  - Spectral gaps in $ \mathit{SU}(d)$
JO  - Comptes Rendus. Mathématique
PY  - 2010
SP  - 609
EP  - 611
VL  - 348
IS  - 11-12
PB  - Elsevier
DO  - 10.1016/j.crma.2010.04.024
LA  - en
ID  - CRMATH_2010__348_11-12_609_0
ER  - 
%0 Journal Article
%A Jean Bourgain
%A Alexander Gamburd
%T Spectral gaps in $ \mathit{SU}(d)$
%J Comptes Rendus. Mathématique
%D 2010
%P 609-611
%V 348
%N 11-12
%I Elsevier
%R 10.1016/j.crma.2010.04.024
%G en
%F CRMATH_2010__348_11-12_609_0
Jean Bourgain; Alexander Gamburd. Spectral gaps in $ \mathit{SU}(d)$. Comptes Rendus. Mathématique, Volume 348 (2010) no. 11-12, pp. 609-611. doi : 10.1016/j.crma.2010.04.024. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.04.024/

[1] P. Bougerol; J. Lacroix Products of Random Matrices with Applications to Schrödinger Operators, Birkhäuser, 1985

[2] J. Bourgain On the Erdos–Volkmann and Katz–Tao ring conjectures, Geom. Funct. Anal., Volume 13 (2003) no. 2, pp. 334-365

[3] J. Bourgain, The discretized ring and projection theorems, J. Anal., in press

[4] J. Bourgain; A. Gamburd On the spectral gap for finitely generated subgroups of SU(2), Invent. Math., Volume 171 (2008) no. 1, pp. 83-121

[5] J. Bourgain; A. Gamburd Expansion and random walks in SLd(Z/pnZ), II, J. Eur. Math. Soc. (JEMS), Volume 11 (2009) no. 5, pp. 1057-1103

[6] E. Breuillard; T. Gelander On dense free subgroups of Lie groups, J. Algebra, Volume 261 (2003) no. 2, pp. 448-467

[7] T. Tao; V. Vu Additive Combinatorics, Cambridge Stud. Adv. Math., vol. 105, 2006

Cited by Sources:

Comments - Policy