Spectral gap in the group of affine transformations over prime fields
Abstract
We study random walks on the semi-direct product of Fpd and SLd(Fp). We estimate the spectral gap in terms of the spectral gap of the projection to the linear part SLd(Fp). This problem is motivated by an analogue in the isometry group of Euclidean space, which have application to smoothness of self-similar measures.
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