A spectral gap theorem in SU$(d)$

Jean Bourgain; Alex Gamburd

doi:10.4171/jems/337

JournalsjemsVol. 14, No. 5pp. 1455–1511

A spectral gap theorem in SU $(d)$

Jean Bourgain
Institute for Advanced Study, Princeton, United States
- MathSciNet
- zbMATH Open
Alex Gamburd
University of California at Santa Cruz, United States
- MathSciNet
- zbMATH Open

Download PDF

Abstract

We establish the spectral gap property for dense subgroups of SU $(d)$ ( $d \geq 2$ ), generated by finitely many elements with algebraic entries; this result was announced in [BG3]. The method of proof differs, in several crucial aspects, from that used in [BG] in the case of SU $(2)$ .

Cite this article

Jean Bourgain, Alex Gamburd, A spectral gap theorem in SU $(d)$ . J. Eur. Math. Soc. 14 (2012), no. 5, pp. 1455–1511

DOI 10.4171/JEMS/337