Spectral gap in the group of affine transformations over prime fields
  We study random walks on the semi-direct product of F_p^d and SL_d(F_p). We estimate the spectral gap in terms of the spectral gap of the projection to the linear part SL_d(F_p). This problem is motivated by an analogue in the isometry group of Euclidean space, which have application to smoothness of self-similar measures. 
Elon Lindenstrauss and Peter P. Varju
math.GR math.CA math.CO