where {Fn, n ∈ N}, is the natural filtration associated to (Xn). We assume that X0 ∈ R d + and that random vectors ξn are such that for all n, Xn ∈ R d + almost surely. The Perron-Frobenius Theorem [10, pp. 3-4] states that M has a positive Perron root ρ. We call Xn “subcritical” if ρ < 1, “supercritical” if ρ > 1 and “critical” if ρ = 1. In the “subcritical” case, one has P(‖Xn‖ → ∞) = 0 becau...

The theory of pseudo circle packings is developed. It generalizes the theory of circle packings. It allows the realization of almost any graph embedding by a geometric structure of circles. The corresponding Thurston’s relaxation mapping is defined and is used to prove the existence and the rigidity of the pseudo circle packing. It is shown that iterates of this mapping, starting from an arbitr...

The theory of pseudo circle packings is developed. It generalizes the theory of circle packings. It allows the realization of almost any graph embedding by a geometric structure of circles. The corresponding Thurston’s relaxation mapping is defined and is used to prove the existence and the rigidity of the pseudo circle packing. It is shown that iterates of this mapping, starting from an arbitr...