Products of random matrices: Dimension and growth in norm

Vladislav Kargin

doi:10.1214/09-AAP658

Products of random matrices: Dimension and growth in norm

Probability 2010-10-20 v2

Authors: Vladislav Kargin

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Abstract

Suppose that $X_1,\...,X_n,\...$ are i.i.d. rotationally invariant $N$ -by- $N$ matrices. Let $\Pi_n=X_n\... X_1$ . It is known that $n^{-1}\log |\Pi_n|$ converges to a nonrandom limit. We prove that under certain additional assumptions on matrices $X_i$ the speed of convergence to this limit does not decrease when the size of matrices, $N$ , grows.

Keywords

random matrices Lyapunov exponent norm growth rotational invariance convergence speed

Cite

@article{arxiv.0903.0632,
  title  = {Products of random matrices: Dimension and growth in norm},
  author = {Vladislav Kargin},
  journal= {arXiv preprint arXiv:0903.0632},
  year   = {2010}
}

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Published in at http://dx.doi.org/10.1214/09-AAP658 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)

Products of random matrices: Dimension and growth in norm

Abstract

Keywords

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