Local spectral gap in simple Lie groups and applications
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | BOUTONNET, Rémi | |
| hal.structure.identifier | Mathematics Department; University of California San Diego | |
| dc.contributor.author | IOANA, Adrian | |
| hal.structure.identifier | Mathematics Department; University of California San Diego | |
| dc.contributor.author | SALEHI-GOLSEFIDI, Alireza | |
| dc.date.accessioned | 2024-04-04T03:11:11Z | |
| dc.date.available | 2024-04-04T03:11:11Z | |
| dc.date.created | 2015 | |
| dc.date.issued | 2016 | |
| dc.identifier.issn | 0020-9910 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/193752 | |
| dc.description.abstractEn | We introduce a novel notion of local spectral gap for general, possibly infinite, measure preserving actions. We establish local spectral gap for the left translation action of Γ on G, whenever Γ is a dense subgroup generated by algebraic elements of an arbitrary connected simple Lie group G. This extends to the non-compact setting works of Bourgain and Gamburd [BG06, BG10], and Benoist and de Saxcé [BdS14]. We present several applications to the Banach-Ruziewicz problem, orbit equivalence rigidity, continuous and monotone expanders, and bounded random walks on G. In particular, we prove that, up to a multiplicative constant, the Haar measure is the unique Γ-invariant finitely additive measure defined on all bounded measurable subsets of G. | |
| dc.language.iso | en | |
| dc.publisher | Springer Verlag | |
| dc.title.en | Local spectral gap in simple Lie groups and applications | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1007/s00222-016-0699-8 | |
| dc.subject.hal | Mathématiques [math]/Théorie des groupes [math.GR] | |
| dc.subject.hal | Mathématiques [math]/Systèmes dynamiques [math.DS] | |
| bordeaux.journal | Inventiones Mathematicae | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-01449823 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01449823v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Inventiones%20Mathematicae&rft.date=2016&rft.eissn=0020-9910&rft.issn=0020-9910&rft.au=BOUTONNET,%20R%C3%A9mi&IOANA,%20Adrian&SALEHI-GOLSEFIDI,%20Alireza&rft.genre=article |
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