Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Scaling in simple continued fraction   We consider a class of real numbers, a subset of irrational numbers and
certain mathematical constants, for which the elements in the simple continued
fraction appears to be random. As an illustrative example, one can consider
$\pi = \{x_0, x_1, x_2, \dots x_n\}$, where $x$'s are the continued fraction
elements computed with an exact value of $\pi$ up to $N$ precision. We
numerically compute probability distribution for the elements and observe a
striking power-law behavior $P(x)\sim x^{-2}$. The statistical analysis
indicates that the elements are uncorrelated and the scaling is robust with
respect to the precision. Our arguments reveal that the underlying mechanism
generating such a scaling may be sample space reducing process.

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The categories of this paper are: plasm-ph
19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
8
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: dg-ga
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: econ
11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph