Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stretch Factor of Long Paths in a planar Poisson-Delaunay Triangulation   Let $X:=X_n\cup\{(0,0),(1,0)\}$, where $X_n$ is a planar Poisson point
process of intensity $n$. We provide a first non-trivial lower bound for the
distance between the expected length of the shortest path between $(0,0)$ and
$(1,0)$ in the Delaunay triangulation associated with $X$ when the intensity of
$X_n$ goes to infinity. Experimental values indicate that the correct value is
about 1.04. We also prove that the expected number of Delaunay edges crossed by
the line segment $[(0,0),(1,0)]$ is equivalent to $2.16\sqrt{n}$ and that the
expected length of a particular path converges to 1.18 giving an upper bound on
the stretch factor.

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The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
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The categories of this paper are: dg-ga
29
The categories of this paper are: funct-an
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The categories of this paper are: hep-th
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The categories of this paper are: bayes-an
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: gr-qc
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The categories of this paper are: adap-org
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: math-ph