Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A product chain without cutoff   In this note, we construct an example of a sequence of $n$-fold product
chains which does not display cutoff for total-variation distance neither for
separation distance. In addition we show that this type of product chains
necessarily displays pre-cutoff.

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The categories of this paper are: cs
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The categories of this paper are: econ
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: stat
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ex
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The categories of this paper are: q-bio
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The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom
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The categories of this paper are: solv-int
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The categories of this paper are: q-alg
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The categories of this paper are: bayes-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: comp-gas