Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A central limit theorem for the variation of the sum of digits   We prove a Central Limit Theorem for probability measures defined via the
variation of the sum-of-digits function, in base b $\ge$ 2. For r $\ge$ 0 and d
$\in$ Z, we consider $\mu$ (r) (d) as the density of integers n $\in$ N for
which the sum of digits increases by d when we add r to n. We give a
probabilistic interpretation of $\mu$ (r) on the probability space given by the
group of b-adic integers equipped with the normalized Haar measure. We split
the base-b expansion of the integer r into so-called "blocks", and we consider
the asymptotic behaviour of $\mu$ (r) as the number of blocks goes to infinity.
We show that, up to renormalization, $\mu$ (r) converges to the standard normal
law as the number of blocks of r grows to infinity. We provide an estimate of
the speed of convergence. The proof relies, in particular, on a $\phi$-mixing
process defined on the b-adic integers.

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The categories of this paper are: cs
26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
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The categories of this paper are: cmp-lg
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The categories of this paper are: dg-ga
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The categories of this paper are: q-alg
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The categories of this paper are: physics
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The categories of this paper are: hep-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: alg-geom
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The categories of this paper are: chao-dyn