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Elon Lindenstrauss; Péter P. Varjú
Spectral gap in the group of affine transformations over prime fields
Annales de la faculté des sciences de Toulouse Sér. 6, 25 no. 5 (2016), p. 969-993, doi: 10.5802/afst.1518
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Résumé - Abstract

Nous étudions les marches aléatoires sur les groupes $\mathbb{F}_p^d\rtimes \rm SL_d(\mathbb{F}_p)$. Nous estimons le trou spectral en fonction du trou spectral de la projection sur la partie linéaire $\rm SL_d(\mathbb{F}_p)$. Ce problème est motivé par son analogue dans le groupe $\mathbb{R}^d\rtimes \rm SO(d)$, qui a des applications à la régularité des mesures auto-similaires.

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