Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The number of distinct adjacent pairs in geometrically distributed
  words: a probabilistic and combinatorial analysis   The analysis of strings of $n$ random variables with geometric distribution
has recently attracted renewed interest: Archibald et al. consider the number
of distinct adjacent pairs in geometrically distributed words. They obtain the
asymptotic ($n\rightarrow\infty$) mean of this number in the cases of different
and identical pairs. In this paper we are interested in all asymptotic moments
in the identical case, in the asymptotic variance in the different case and in
the asymptotic distribution in both cases. We use two approaches: the first
one, the probabilistic approach, leads to variances in both cases and to some
conjectures on all moments in the identical case and on the distribution in
both cases. The second approach, the combinatorial one, relies on multivariate
pattern matching techniques, yielding exact formulas for first and second
moments. We use such tools as Mellin transforms, Analytic Combinatorics, Markov
Chains.

13
The categories of this paper are: quant-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
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The categories of this paper are: nucl-ex
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The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
8
The categories of this paper are: hep-ex
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The categories of this paper are: adap-org
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The categories of this paper are: math-ph
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The categories of this paper are: stat
10
The categories of this paper are: q-bio