Products of random matrices: Dimension and growth in norm

Details Products of random matrices: Dimension and growth in norm Products of random matrices: Dimension and growth in norm

2009-03-03

arxiv.org/abs/0903.0632v2

Annals of Applied Probability 2010, Vol. 20, No. 3, 890-906

Mathematics

Probability

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

Scientific paper

10.1214/09-AAP658

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.

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