Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Asymptotics of finite system Lyapunov exponents for some random matrix
  ensembles   For products $P_N$ of $N$ random matrices of size $d \times d$, there is a
natural notion of finite $N$ Lyapunov exponents $\{\mu_i\}_{i=1}^d$. In the
case of standard Gaussian random matrices with real, complex or real quaternion
elements, and extended to the general variance case for $\mu_1$, methods known
for the computation of $\lim_{N \to \infty} \langle \mu_i \rangle$ are used to
compute the large $N$ form of the variances of the exponents. Analogous
calculations are performed in the case that the matrices making up $P_N$ are
products of sub-blocks of random unitary matrices with Haar measure.
Furthermore, we make some remarks relating to the coincidence of the Lyapunov
exponents and the stability exponents relating to the eigenvalues of $P_N$.

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The categories of this paper are: acc-phys
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The categories of this paper are: hep-lat
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The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: stat
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The categories of this paper are: funct-an
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The categories of this paper are: nlin
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
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The categories of this paper are: patt-sol
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The categories of this paper are: adap-org
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The categories of this paper are: physics
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The categories of this paper are: hep-ex
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The categories of this paper are: atom-ph
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The categories of this paper are: q-fin