Asymptotic Lyapunov exponents for large random matrices.(English)Zbl 1386.60027
Summary: Suppose that \(A_{1},\ldots ,A_{N}\) are independent random matrices of size \(n\) whose entries are i.i.d. copies of a random variable \(\xi \) of mean zero and variance one. It is known from the late 1980s that when \(\xi \) is Gaussian then \(N^{-1}\log \| A_{N}\ldots A_{1}\| \) converges to \(\log \sqrt{n}\) as \(N\rightarrow \infty \). We will establish similar results for more general matrices with explicit rate of convergence. Our method relies on a simple interplay between additive structures and growth of matrices.
MSC:
| 60B20 | Random matrices (probabilistic aspects) |
| 60B10 | Convergence of probability measures |
| 15B52 | Random matrices (algebraic aspects) |
Cite
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