Fluctuations of the Product of Random Matrices and Generalized Lyapunov Exponent

@article{Texier2019FluctuationsOT,
  title={Fluctuations of the Product of Random Matrices and Generalized Lyapunov Exponent},
  author={Christophe Texier},
  journal={arXiv: Mathematical Physics},
  year={2019}
}
  • C. Texier
  • Published 19 July 2019
  • Mathematics
  • arXiv: Mathematical Physics
I present a general framework allowing to carry out explicit calculation of the moment generating function of random matrix products $\Pi_n=M_nM_{n-1}\cdots M_1$, where $M_i$'s are i.i.d.. Following Tutubalin [Theor. Probab. Appl. {\bf 10}, 15 (1965)], the calculation of the generating function is reduced to finding the largest eigenvalue of a certain transfer operator associated with a family of representations of the group. The formalism is illustrated by considering products of random… 

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