Comptes Rendus
Group Theory
Spectral gaps in SU(d)
[Trou spectral dans 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.

Reçu le :
Accepté le :
Publié le :
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

  • Somnath Chakraborty Random ϵ-cover on compact Riemannian symmetric space, Journal of Lie Theory, Volume 34 (2024) no. 1, pp. 137-169 | Zbl:1554.43010
  • Alexander Gamburd Arithmetic and dynamics on varieties of Markoff type, International congress of mathematicians 2022, ICM 2022, Helsinki, Finland, virtual, July 6–14, 2022. Volume 3. Sections 1–4, Berlin: European Mathematical Society (EMS), 2023, pp. 1800-1836 | DOI:10.4171/icm2022/191 | Zbl:1551.14103
  • Federico Vigolo Measure expanding actions, expanders and warped cones, Transactions of the American Mathematical Society, Volume 371 (2019) no. 3, pp. 1951-1979 | DOI:10.1090/tran/7368 | Zbl:1402.05205
  • Alex Bocharov; Martin Roetteler; Krysta M. Svore Factoring with qutrits: Shor's algorithm on ternary and metaplectic quantum architectures, Physical Review A, Volume 96 (2017) no. 1 | DOI:10.1103/physreva.96.012306
  • Pravesh K. Kothari; Raghu Meka Almost optimal pseudorandom generators for spherical caps (extended abstract), Proceedings of the 47th annual ACM symposium on theory of computing, STOC '15, Portland, OR, USA, June 14–17, 2015, New York, NY: Association for Computing Machinery (ACM), 2015, pp. 247-256 | DOI:10.1145/2746539.2746611 | Zbl:1321.65008
  • Jean-Pierre Conze; Y. Guivarc'h Ergodicity of group actions and spectral gap, applications to random walks and Markov shifts, Discrete Continuous Dynamical Systems - A, Volume 33 (2013) no. 9, p. 4239 | DOI:10.3934/dcds.2013.33.4239
  • J. Bourgain On the Furstenberg measure and density of states for the Anderson-Bernoulli model at small disorder, Journal d'Analyse Mathématique, Volume 117 (2012), pp. 273-295 | DOI:10.1007/s11854-012-0022-6 | Zbl:1275.82006
  • Jean Bourgain; Alex Gamburd A spectral gap theorem in SU(d), Journal of the European Mathematical Society (JEMS), Volume 14 (2012) no. 5, pp. 1455-1511 | DOI:10.4171/jems/337 | Zbl:1254.43010
  • Jean-Pierre Conze; Stéphane Le Borgne Quenched central limit theorem for random walks with a spectral gap, Comptes Rendus. Mathématique. Académie des Sciences, Paris, Volume 349 (2011) no. 13-14, pp. 801-805 | DOI:10.1016/j.crma.2011.06.017 | Zbl:1225.60040

Cité par 9 documents. Sources : Crossref, zbMATH

Commentaires - Politique


Il n'y a aucun commentaire pour cet article. Soyez le premier à écrire un commentaire !


Publier un nouveau commentaire:

Publier une nouvelle réponse: