Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Shortest Path through Random Points   Let $(M,g_1)$ be a complete $d$-dimensional Riemannian manifold for $d > 1$.
Let $\mathcal X_n$ be a set of $n$ sample points in $M$ drawn randomly from a
smooth Lebesgue density $f$ supported in $M$. Let $x,y$ be two points in $M$.
We prove that the normalized length of the power-weighted shortest path between
$x, y$ through $\mathcal X_n$ converges almost surely to a constant multiple of
the Riemannian distance between $x,y$ under the metric tensor $g_p =
f^{2(1-p)/d} g_1$, where $p > 1$ is the power parameter.

7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex