Lyapunov Exponents for Products of Complex Gaussian Random Matrices |
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| Authors: | Peter J. Forrester |
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| Affiliation: | 1. Department of Mathematics and Statistics, The University of Melbourne, Melbourne, VIC, 3010, Australia
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| 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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