Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The dimension of the St. Petersburg game   Let $S_n$ be the total gain in $n$ repeated St.\ Petersburg games. It is
known that $n^{-1}(S_n-n\log_2n)$ converges in distribution to a random element
$Y(t)$ along subsequences of the form $k(n)=2^{p(n)}t(n)$ with
$p(n)=\lceil\log_2k(n)\rceil\to\infty$ and $t(n)\to t\in[\frac12,1]$. We
determine the Hausdorff and box-counting dimension of the range and the graph
for almost all sample paths of the stochastic process $\{Y(t)\}_{t\in[1/2,1]}$.
The results are compared to the fractal dimension of the corresponding limiting
objects when gains are given by a deterministic sequence initiated by Hugo
Steinhaus.

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The categories of this paper are: funct-an
18
The categories of this paper are: econ
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The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
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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: mtrl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: astro-ph
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
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The categories of this paper are: q-fin
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The categories of this paper are: cmp-lg
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The categories of this paper are: ao-sci