For i.i.d. products of invertible complex matrices, the normalized log of the spectral radius converges almost surely to the first Lyapunov exponent under a finite second moment, and in L^1 under a finite first moment, without any irreducibility assumption.
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Law of large numbers for the spectral radius of random matrix products
For i.i.d. products of invertible complex matrices, the normalized log of the spectral radius converges almost surely to the first Lyapunov exponent under a finite second moment, and in L^1 under a finite first moment, without any irreducibility assumption.