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
Alex Gamburd
University of California at Santa Cruz, United States

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