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• W4377029089 abstract "Let $G$ be a connected semisimple real algebraic group, and $Gamma<G$ be a Zariski dense Anosov subgroup with respect to a minimal parabolic subgroup. We describe the asymptotic behavior of matrix coefficients $langle (exp tv). f_1, f_2rangle$ in $L^2(Gammabackslash G)$ as $tto infty$ for any $f_1, f_2in C_c(Gammabackslash G)$ and any vector $v$ in the interior of the limit cone of $Gamma$. These asymptotics involve higher rank analogues of Burger-Roblin measures which are introduced in this paper. As an application, for any affine symmetric subgroup $H$ of $G$, we obtain a bisector counting result for $Gamma$-orbits with respect to the corresponding generalized Cartan decomposition of $G$. Moreover, we obtain analogues of the results of Duke-Rudnick-Sarnak and Eskin-McMullen for counting discrete $Gamma$-orbits in affine symmetric spaces $Hbackslash G$." @default.
• W4377029089 created "2023-05-19" @default.
• W4377029089 creator A5008742142 @default.
• W4377029089 creator A5054801365 @default.
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• W4377029089 date "2023-05-16" @default.
• W4377029089 modified "2023-09-30" @default.
• W4377029089 title "Anosov groups: local mixing, counting and equidistribution" @default.
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• W4377029089 doi "https://doi.org/10.2140/gt.2023.27.513" @default.
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