Let $G$ be a connected semisimple real algebraic group, and $GammaG$ 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 and Sarnak as well as Eskin and McMullen for counting discrete $Gamma$--orbits in affine symmetric spaces $Hbackslash G$.
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