Degenerations of SL(2,) representations and Lyapunov exponents
Annales Henri Lebesgue, Volume 2 (2019), pp. 515-565.



We study the asymptotic behavior of the Lyapunov exponent in a meromorphic family of random products of matrices in SL(2,), 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 1 ().


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