Spectral gap properties for linear random walks and Pareto's asymptotics for affine stochastic recursions

Yves Guivarc'H, Emile Le Page

Let $V={\mathbb{R}}^d$ be the Euclidean $d$-dimensional space, $\mu$ (resp $\lambda$) a probability measure on the linear (resp affine) group $G=GL(V)$ (resp $H= \Aff (V))$ and assume that…