Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Connectivity of sparse Bluetooth networks   Consider a random geometric graph defined on $n$ vertices uniformly
distributed in the $d$-dimensional unit torus. Two vertices are connected if
their distance is less than a "visibility radius" $r_n$. We consider {\sl
Bluetooth networks} that are locally sparsified random geometric graphs. Each
vertex selects $c$ of its neighbors in the random geometric graph at random and
connects only to the selected points. We show that if the visibility radius is
at least of the order of $n^{-(1-\delta)/d}$ for some $\delta > 0$, then a
constant value of $c$ is sufficient for the graph to be connected, with high
probability. It suffices to take $c \ge \sqrt{(1+\epsilon)/\delta} + K$ for any
positive $\epsilon$ where $K$ is a constant depending on $d$ only. On the other
hand, with $c\le \sqrt{(1-\epsilon)/\delta}$, the graph is disconnected, with
high probability.

35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom