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Analyticity and other properties of the largest or smallest Lyapunov exponentof a product of real matrices with a "cone property" are studied as functionsof the matrices entries, as long as they vary without destroying the coneproperty. The result is applied to stability directions, Lyapunov coefficientsand Lyapunov exponents of a class of products of random matrices and ofdynamical systems. The method is based on the classical theory of the Mayerseries in Statistical Mechanics of rarefied gases.

Random matrices and Lyapunov coefficients regularity