Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Szemer\'edi's theorem with differences from a random set   We consider, over both the integers and finite fields, Szemer\'{e}di's
theorem on $k$-term arithmetic progressions where the set $S$ of allowed common
differences in those progressions is restricted and random. Fleshing out a line
of enquiry suggested by Frantzikinakis et al, we show that over the integers,
the conjectured threshold for $\mathbb{P}(d \in S)$ for Szemer\'{e}di's theorem
to hold a.a.s follows from a conjecture about how so-called dual functions are
approximated by nilsequences. We also show that the threshold over finite
fields is different to this threshold over the integers.

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The categories of this paper are: chao-dyn
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The categories of this paper are: stat
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-lat
0
The categories of this paper are: hep-ph
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The categories of this paper are: math-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: cmp-lg
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The categories of this paper are: solv-int
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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: q-fin
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The categories of this paper are: ao-sci
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The categories of this paper are: eess
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The categories of this paper are: quant-ph