Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Asymptotic of geometrical navigation on a random set of points of the
  plane   A navigation on a set of points $S$ is a rule for choosing which point to
move to from the present point in order to progress toward a specified target.
We study some navigations in the plane where $S$ is a non uniform Poisson point
process (in a finite domain) with intensity going to $+\infty$. We show the
convergence of the traveller path lengths, the number of stages done, and the
geometry of the traveller trajectories, uniformly for all starting points and
targets, for several navigations of geometric nature. Other costs are also
considered. This leads to asymptotic results on the stretch factors of random
Yao-graphs and random $\theta$-graphs.

29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph