Let G be a finitely generated group endowed with some probability measure μ and $(\rho_{\lambda})$ be a non-compact algebraic family of representations of G into SL(2,C). This gives rise to a random product of matrices depending on the parameter λ, so the upper Lyapunov exponent defines a function on the parameter space. Using techniques from non-Archimedean analysis and algebraic geometry, we study the asymptotics of the Lyapunov exponent when λ goes to infinity. This is joint work with Charles Favre.
Fanny Kassel