Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Polynomial mixing time of edge flips on quadrangulations   We establish the first polynomial upper bound for the mixing time of random
edge flips on rooted quadrangulations: we show that the spectral gap of the
edge flip Markov chain on quadrangulations with $n$ faces admits, up to
constants, an upper bound of $n^{-5/4}$ and a lower bound of $n^{-11/2}$. In
order to obtain the lower bound, we also consider a very natural Markov chain
on plane trees (or, equivalently, on Dyck paths) and improve the previous lower
bound for its spectral gap obtained by Shor and Movassagh.

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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: hep-ex
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The categories of this paper are: nucl-ex
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The categories of this paper are: math-ph
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The categories of this paper are: adap-org
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The categories of this paper are: cs
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The categories of this paper are: ao-sci
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The categories of this paper are: chem-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: acc-phys
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The categories of this paper are: comp-gas
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The categories of this paper are: solv-int
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The categories of this paper are: q-alg