Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Long Range Percolation Mixing Time   We provide an estimate, sharp up to poly-logarithmic factors, of the
asymptotically almost sure mixing time of the graph created by long-range
percolation on the cycle of length N (Z/NZ). While it is known that the almost
sure diameter drops from linear to poly-logarithmic as the exponent s decreases
below 2, the almost sure mixing time drops from N^2 only to N^(s-1) (up to
poly-logarithmic factors).

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The categories of this paper are: comp-gas
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The categories of this paper are: acc-phys
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The categories of this paper are: cmp-lg
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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: nlin
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The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-ex
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The categories of this paper are: funct-an
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The categories of this paper are: hep-lat
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The categories of this paper are: ao-sci
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The categories of this paper are: cs
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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: atom-ph
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The categories of this paper are: mtrl-th