Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Walking on the Edge and Cosystolic Expansion   Random walks on regular bounded degree expander graphs have numerous
applications. A key property of these walks is that they converge rapidly to
the uniform distribution on the vertices. The recent study of expansion of high
dimensional simplicial complexes, which are the high dimensional analogues of
graphs, calls for the natural generalization of random walks to higher
dimensions. In particular, a high order random walk on a $2$-dimensional
simplicial complex moves at random between neighboring edges of the complex,
where two edges are considered neighbors if they share a common triangle. We
show that if a regular $2$-dimensional simplicial complex is a cosystolic
expander and the underlying graph of the complex has a spectral gap larger than
$1/2$, then the random walk on the edges of the complex converges rapidly to
the uniform distribution on the edges.

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The categories of this paper are: funct-an
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The categories of this paper are: econ
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The categories of this paper are: comp-gas
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The categories of this paper are: chem-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: q-fin
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The categories of this paper are: chao-dyn
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The categories of this paper are: dg-ga
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The categories of this paper are: quant-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-lat
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The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat