Abstract
The exact value of the Lyapunov exponents for the random matrix product P N =A N A N−1⋯A 1 with each \(A_{i} = \varSigma^{1/2} G_{i}^{\mathrm{c}}\), where Σ is a fixed d×d positive definite matrix and \(G_{i}^{\mathrm{c}}\) a d×d complex Gaussian matrix with entries standard complex normals, are calculated. Also obtained is an exact expression for the sum of the Lyapunov exponents in both the complex and real cases, and the Lyapunov exponents for diffusing complex matrices.
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Thanks are due to one of the referees, for providing a list of otherwise hard to catch typographical errors. This work was supported by the Australian Research Council.
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Forrester, P.J. Lyapunov Exponents for Products of Complex Gaussian Random Matrices. J Stat Phys 151, 796–808 (2013). https://doi.org/10.1007/s10955-013-0735-7
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DOI: https://doi.org/10.1007/s10955-013-0735-7