Given a finite set of quasi-periodic cocycles the random product them is defined as composition according to some probability measure. We prove that $C^r$, $0\leq r \leq \infty$ (or analytic) $k+1$-tuples quasi periodic taking values in $SL_2(\mathbb{R})$ such has positive Lyapunov exponent contains $C^0$ open and $C^r$ dense subset which formed by continuity point For $GL_d(\mathbb{R})$ fo...

The free convolution ⊞ is the binary operation on the set of probability measures on the real line which allows to deduce, from the individual spectral distributions, the spectral distribution of a sum of independent unitarily invariant square random matrices or of a sum of free operators in a non commutative probability space. In the same way, the rectangular free convolution ⊞ λ allows to ded...

Measure Differential Equations (MDE) describe the evolution of probability measures driven by velocity fields, i.e. on tangent bundle. They are, one side, a measure-theoretic generalization ordinary differential equations; other they allow to concentration and diffusion phenomena typical kinetic equations. In this paper, we analyze some properties class equations, e...