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Statistical Properties of T-exponential and Random Matrices Products

Student: Darovskikh Igor

Supervisor: Kirill Zybin

Faculty: Faculty of Mathematics

Educational Programme: Mathematics (Bachelor)

Year of Graduation: 2017

Current paper contains the solution to the problem of finding the Lyapunov spectrum and the generalized Lyapunov exponents of the continuous isotropic stationary matrix processes with a finite correlation time. There was obtained the explicit formula to those quantities, that depends on the cumulant function of the initial process. It was also studied the discrete analogue to the problem stated and the methods to calculate LS and GLE of a discrete random matrix process were given. We obtained the conditions, when the formulas for the continuous problem could be used in a discrete case. There was also given the counterexample, illustrating the aforementioned techniques of calculating LS in both discrete and continuous case, and it was shown, that if the found conditions are not met, there appear different answers.

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