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Let $\Gamma$ be a discrete subgroup of $\textrm{PGL}(d,\R)$ and fix someeuclidean norm $\|\ \|$ on $\R^d.$ Let $N_\Gamma(t)$ be the number of elementsin $\Gamma$ whose operator norm is $\leq t.$ In this article we prove anasymptotic for the growth of $N_\Gamma(t)$ when $t\to\infty$ for a class of$\Gamma$'s which contains, in particular, Hitchin representations of surfacegroups and groups dividing a convex set of $\P(\R^d).$ We also prove analoguecounting theorems for the growth of the spectral radii. More preciseinformation is given for Hitchin representations.

Quantitative properties of convex representations