Citation
P. Balister, B. Bollobas. "Random transceiver networks". Adv. in Appl. Probab., 41(2):323-343, 2009.

Abstract
In the paper we consider randomly scattered radio transceivers ind dimensions (in practical applications, in the plane or three dimensional space) each of which can transmit signals to all transceivers in a given randomly chosen region about itself. If a signal is retransmitted by every transceiver that receives it, under what circumstances will a signal propagate to a large distance from its starting point. Put more formally, place points x(1), x(2), ... in space according to a Poisson process with intensity 1. Then, independently for each point x(i), choose a bounded region A(i) from some fixed distribution and let G be the random directed graph with vertex set x(i) and edges x(i)x(j) whenever x(j) is in x(i)+A(i). In the paper we show that for any positive eta, if the regions x(i)+A(i) do not overlap too much (in a sense that we shall make precise), then G has an infinite directed path provided the expected number of transceivers that can receive a signal directly from x(i) is at least 1+. One example where these conditions hold, and we obtain percolation, is in dimension d with A(i) a hypersphere of volume 1+, where  tends to zero as d tends to infinity. Another example is in two dimensions, where A(i) are randomly oriented sectors of a disk of a given angle and area 1+.

Electronic downloads

• http://projecteuclid.org/euclid.aap/1246886613

• HTML

  P. Balister, B. Bollobas. <a
  href="http://chess.eecs.berkeley.edu/pubs/760.html"
  >Random transceiver networks</a>, <i>Adv. in
  Appl. Probab.</i>, 41(2):323-343,  2009.

• Plain text

  P. Balister, B. Bollobas. "Random transceiver
  networks". <i>Adv. in Appl. Probab.</i>,
  41(2):323-343,  2009.

• BibTeX

  @article{BalisterBollobas09_RandomTransceiverNetworks,
      author = {P. Balister and B. Bollobas},
      title = {Random transceiver networks},
      journal = {Adv. in Appl. Probab.},
      volume = {41},
      number = {2},
      pages = {323-343},
      year = {2009},
      abstract = { In the paper we consider randomly scattered radio
                transceivers ind dimensions (in practical
                applications, in the plane or three dimensional
                space) each of which can transmit signals to all
                transceivers in a given randomly chosen region
                about itself. If a signal is retransmitted by
                every transceiver that receives it, under what
                circumstances will a signal propagate to a large
                distance from its starting point. Put more
                formally, place points x(1), x(2), ... in space
                according to a Poisson process with intensity 1.
                Then, independently for each point x(i), choose a
                bounded region A(i) from some fixed distribution
                and let G be the random directed graph with vertex
                set x(i) and edges x(i)x(j) whenever x(j) is in
                x(i)+A(i). In the paper we show that for any
                positive eta, if the regions x(i)+A(i) do not
                overlap too much (in a sense that we shall make
                precise), then G has an infinite directed path
                provided the expected number of transceivers that
                can receive a signal directly from x(i) is at
                least 1+�. One example where these conditions
                hold, and we obtain percolation, is in dimension d
                with A(i) a hypersphere of volume 1+�, where �
                tends to zero as d tends to infinity. Another
                example is in two dimensions, where A(i) are
                randomly oriented sectors of a disk of a given
                angle and area 1+�.},
      URL = {http://chess.eecs.berkeley.edu/pubs/760.html}
  }
  

Posted by Christopher Brooks on 4 Nov 2010.
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