Spectral gaps in $ \mathit{SU}(d)$

Jean Bourgain; Alexander Gamburd

doi:10.1016/j.crma.2010.04.024

Group Theory

Spectral gaps in

SU (d)

[Trou spectral dans

SU (d)

]

Présenté par : Jean Bourgain

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

Comptes Rendus. Mathématique, Volume 348 (2010) no. 11-12, pp. 609-611.

Résumé
Abstract

On démontre que si $g_{1}, \dots, g_{k}$ sont des éléments algébriques de $SU (d)$ et le groupe engendré par $g_{1}, \dots, g_{k}$ est dense, alors l'opérateur de Hecke défini par ces éléments a un trou spectral.

It is shown that if $g_{1}, \dots, g_{k}$ are algebraic elements in $SU (d)$ generating a dense subgroup, then the corresponding Hecke operator has a spectral gap.

Reçu le : 2010-04-09
Accepté le : 2010-04-15
Publié le : 2010-05-04

DOI : 10.1016/j.crma.2010.04.024

Affiliations des auteurs :

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

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     title = {Spectral gaps in $ \mathit{SU}(d)$},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {609--611},
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     number = {11-12},
     year = {2010},
     doi = {10.1016/j.crma.2010.04.024},
     language = {en},
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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/

Bibliographie
Cité par

[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 ${SL}_{d} (Z / p^{n} Z)$ , 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

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
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) no. 1, p. 273 | DOI:10.1007/s11854-012-0022-6

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