Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Optimal Cheeger cuts and bisections of random geometric graphs   Let $d \geq 2$. The Cheeger constant of a graph is the minimum
surface-to-volume ratio of all subsets of the vertex set with relative volume
at most 1/2. There are several ways to define surface and volume here: the
simplest method is to count boundary edges (for the surface) and vertices (for
the volume). We show that for a geometric (possibly weighted) graph on $n$
random points in a $d$-dimensional domain with Lipschitz boundary and with
distance parameter decaying more slowly (as a function of $n$) than the
connectivity threshold, the Cheeger constant (under several possible
definitions of surface and volume), also known as conductance, suitably
rescaled, converges for large $n$ to an analogous Cheeger-type constant of the
domain. Previously, Garc\'ia Trillos {\em et al.} had shown this for $d \geq 3$
but had required an extra condition on the distance parameter when $d=2$.

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The categories of this paper are: eess
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The categories of this paper are: nucl-ex
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The categories of this paper are: cs
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The categories of this paper are: plasm-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: supr-con
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The categories of this paper are: hep-ex
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The categories of this paper are: funct-an
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The categories of this paper are: solv-int
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The categories of this paper are: nlin
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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: math-ph