Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The hit-and-run version of top-to-random   We study an example of a {\em hit-and-run} random walk on the symmetric group
$\mathbf S_n$. Our starting point is the well understood {\em top-to-random}
shuffle. In the hit-and-run version, at each {\em single step}, after picking
the point of insertion, $j$, uniformly at random in $\{1,\dots,n\}$, the top
card is inserted in the $j$-th position $k$ times in a row where $k$ is uniform
in $\{0,1,\dots,j-1\}$. The question is, does this accelerate mixing
significantly or not? We show that, in $L^2$ and sup-norm, this accelerates
mixing at most by a constant factor (independent of $n$). Analyzing this
problem in total variation is an interesting open question.

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The categories of this paper are: cond-mat
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The categories of this paper are: mtrl-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
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The categories of this paper are: adap-org
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The categories of this paper are: bayes-an
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The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
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The categories of this paper are: gr-qc
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The categories of this paper are: funct-an
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The categories of this paper are: nlin
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The categories of this paper are: chem-ph