Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lyapunov exponent and variance in the CLT for products of random
  matrices related to random Fibonacci sequences   We consider three matrix models of order 2 with one random entry $\epsilon$
and the other three entries being deterministic. In the first model, we let
$\epsilon\sim\textrm{Bernoulli}\left(\frac{1}{2}\right)$. For this model we
develop a new technique to obtain estimates for the top Lyapunov exponent in
terms of a multi-level recursion involving Fibonacci-like sequences. This in
turn gives a new characterization for the Lyapunov exponent in terms of these
sequences. In the second model, we give similar estimates when
$\epsilon\sim\textrm{Bernoulli}\left(p\right)$ and $p\in [0,1]$ is a parameter.
Both of these models are related to random Fibonacci sequences. In the last
model, we compute the Lyapunov exponent exactly when the random entry is
replaced with $\xi\epsilon$ where $\epsilon$ is a standard Cauchy random
variable and $\xi$ is a real parameter. We then use Monte Carlo simulations to
approximate the variance in the CLT for both parameter models.

15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
17
The categories of this paper are: q-fin