Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Lyapunov exponent of products of random $2\times2$ matrices close to
  the identity   We study products of arbitrary random real $2 \times 2$ matrices that are
close to the identity matrix. Using the Iwasawa decomposition of
$\text{SL}(2,{\mathbb R})$, we identify a continuum regime where the mean
values and the covariances of the three Iwasawa parameters are simultaneously
small. In this regime, the Lyapunov exponent of the product is shown to assume
a scaling form. In the general case, the corresponding scaling function is
expressed in terms of Gauss' hypergeometric function. A number of particular
cases are also considered, where the scaling function of the Lyapunov exponent
involves other special functions (Airy, Bessel, Whittaker, elliptic). The
general solution thus obtained allows us, among other things, to recover in a
unified framework many results known previously from exactly solvable models of
one-dimensional disordered systems.

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The categories of this paper are: q-bio
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The categories of this paper are: hep-lat
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The categories of this paper are: gr-qc
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The categories of this paper are: supr-con
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The categories of this paper are: atom-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: nlin
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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: adap-org
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The categories of this paper are: mtrl-th
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The categories of this paper are: cs
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The categories of this paper are: physics
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The categories of this paper are: chem-ph