Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Continuum Line-of-Sight Percolation on Poisson-Voronoi Tessellations   In this work, we study a new model for continuum line-of-sight percolation in
a random environment driven by the Poisson-Voronoi tessellation in the
$d$-dimensional Euclidean space. The edges (one-dimensional facets, or simply
1-facets) of this tessellation are the support of a Cox point process, while
the vertices (zero-dimensional facets or simply 0-facets) are the support of a
Bernoulli point process. Taking the superposition $Z$ of these two processes,
two points of $Z$ are linked by an edge if and only if they are sufficiently
close and located on the same edge (1-facet) of the supporting tessellation. We
study the percolation of the random graph arising from this construction and
prove that a 0-1 law, a subcritical phase as well as a supercritical phase
exist under general assumptions. Our proofs are based on a coarse-graining
argument with some notion of stabilization and asymptotic essential
connectedness to investigate continuum percolation for Cox point processes. We
also give numerical estimates of the critical parameters of the model in the
planar case, where our model is intended to represent telecommunications
networks in a random environment with obstructive conditions for signal
propagation.

37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph