Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Random gap processes and asymptotically complete sequences   We study a process of generating random positive integer weight sequences $\{
W_n \}$ where the gaps between the weights $\{ X_n = W_n - W_{n-1} \}$ are
i.i.d. positive integer-valued random variables. We show that as long as the
gap distribution has finite $\frac{1}{2}$-moment, almost surely, the resulting
weight sequence is asymptotically complete, i.e., all large enough multiples of
the gcd of the possible gap values can be written as a sum of distinct weights.
We then show a much stronger result that if the gap distribution has a moment
generating function with large enough radius of convergence, then every large
enough multiple of the gcd of gap values can be written as a sum of $m$
distinct weights for any fixed $m \geq 2$.

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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: atom-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: cs
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The categories of this paper are: mtrl-th
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The categories of this paper are: eess
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The categories of this paper are: supr-con
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The categories of this paper are: q-fin
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The categories of this paper are: physics
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The categories of this paper are: math-ph
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The categories of this paper are: funct-an
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The categories of this paper are: adap-org