Dujardin, Romain; Favre, Charles
Degenerations of $\mathrm{SL}\left(2,ℂ\right)$ representations and Lyapunov exponents
Annales Henri Lebesgue, Volume 2 (2019), p. 515-565

### Abstract

We study the asymptotic behavior of the Lyapunov exponent in a meromorphic family of random products of matrices in $\mathrm{SL}\left(2,ℂ\right)$, as the parameter converges to a pole. We show that the blow-up of the Lyapunov exponent is governed by a quantity which can be interpreted as the non-Archimedean Lyapunov exponent of the family. We also describe the limit of the corresponding family of stationary measures on ${ℙ}^{1}\left(ℂ\right)$.

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