Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An elementary proof that random Fibonacci sequences grow exponentially   We consider random Fibonacci sequences given by $x_{n+1}=\pm \beta
x_{n}+x_{n-1}$. Viswanath (\cite{viswanath}), following Furstenberg
(\cite{furst}) showed that when $\beta = 1$, $\lim_{n\to
\infty}|x_{n}|^{1/n}=1.13...$, but his proof involves the use of floating point
computer calculations. We give a completely elementary proof that $1.25577 \ge
(E(|x_{n}|))^{1/n} \ge 1.12095$ where $E(|x_{n}|)$ is the expected value for
the absolute value of the $n$th term in a random Fibonacci sequence. We compute
this expected value using recurrence relations which bound the sum of all
possible $n$th terms for such sequences. In addition, we give upper an lower

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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-ex
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The categories of this paper are: funct-an
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The categories of this paper are: econ
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The categories of this paper are: mtrl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: supr-con
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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: cmp-lg
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The categories of this paper are: ao-sci
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The categories of this paper are: nlin
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The categories of this paper are: hep-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: cs
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The categories of this paper are: q-fin