A Spectral Gap Theorem in $SU(d)$
  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). 
Jean Bourgain and Alex Gamburd
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