Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Hostname: page-component-84b7d79bbc-l82ql Total loading time: 0 Render date: 2024-07-29T20:24:55.357Z Has data issue: false hasContentIssue false

References

Published online by Cambridge University Press:  05 November 2012

Martin Haenggi
Martin Haenggi
Affiliation:
University of Notre Dame, Indiana
Get access

Summary

A summary is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content.
Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Chapter
Information
Stochastic Geometry for Wireless Networks , pp. 275 - 280
Publisher: Cambridge University Press
Print publication year: 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Alon, N. & Spencer, J. (2008), The Probabilistic Method, 3rd edn., Wiley.CrossRefGoogle Scholar
Andrews, J. G., Baccelli, F. & Ganti, R. K. (2011), A tractable approach to coverage and rate in cellular networks, IEEE Transactions on Communications 59(11), 3122–3134.CrossRefGoogle Scholar
Athreya, K. B. & Ney, P. E. (2004), Branching Processes, Dover Publications.Google Scholar
Baccelli, F. & Blaszczyszyn, B. (2009), Stochastic Geometry and Wireless Networks, NOW.Google Scholar
Baccelli, F., Blaszczyszyn, B. & Mirsadeghi, M. O. H. (2011), Optimal paths on the space–time SINR random graph, Advances in Applied Probability 43(1), 131–150.CrossRefGoogle Scholar
Baccelli, F., Blaszczyszyn, B. & Mühlethaler, P. (2006), An ALOHA protocol for multihop mobile wireless networks, IEEE Transactions on Information Theory 52(2), 421–436.CrossRefGoogle Scholar
Baddeley, A. J. & Silverman, B. W. (1984), A cautionary example on the use of second-order methods for analyzing point patterns, Biometrics 40(4), 1089–1093.CrossRefGoogle Scholar
Baddeley, A. & Turner, R. (2005), Spatstat: an R package for analyzing spatial point patterns, Journal of Statistical Software 12(6), 1–42.CrossRefGoogle Scholar
Baddeley, A. J. & van Lieshout, M. N. M. (1995), Area-interaction point processes, Annals of the Institute of Statistical Mathematics 47(4), 601–619.CrossRefGoogle Scholar
Baddeley, A., Bárány, I., Schneider, R. & Weil, W. (2007), Stochastic Geometry, Springer.Google Scholar
Balister, P., Bollobás, B., Sarkar, A. & Walters, M. (2005), Connectivity of random k-nearest-neighbor graphs, Advances in Applied Probability 37, 1–24.CrossRefGoogle Scholar
Balister, P., Bollobás, B., Sarkar, A. & Walters, M. (2010), Sentry selection in wireless networks, Advances in Applied Probability 42(1), 1–25.CrossRefGoogle Scholar
Balister, P., Bollobás, B. & Walters, M. (2004), Continuum percolation with steps in an annulus, Annals of Applied Probability 14, 1869–1879.CrossRefGoogle Scholar
Balister, P., Bollobás, B. & Walters, M. (2005), Continuum percolation with steps in the square or the disc, Random Structures and Algorithms 26(4), 392–403.CrossRefGoogle Scholar
Barbour, A. D. & Chen, L. H. Y. (2005), Stein's Method and Applications, SingaporeUniversity Press.CrossRefGoogle Scholar
Bedford, T. & van den Berg, J. (1997), A remark on the Van Lieshout and Baddeley J function for point processes, Advances in Applied Probability 29(1), 19–25.CrossRefGoogle Scholar
Bollobás, B. (2001), Random Graphs, 2nd edn., Cambridge University Press.CrossRefGoogle Scholar
Bollobás, B. & Riordan, O. (2006), Percolation, Cambridge University Press.CrossRefGoogle Scholar
Broadbent, S. & Hammersley, J. (1957), Percolation processes I. Crystals and mazes, Proceedings of the Cambridge Philosophical Society 53, 629–641.CrossRefGoogle Scholar
Campbell, N. (1909), The study of discontinuous phenomena, Mathematical Proceedings of the Cambridge Philosophical Society 15, 117–136.Google Scholar
Cressie, N. (1993), Statistics for Spatial Data, revised edn., Wiley.Google Scholar
Daley, D. J. & Vere-Jones, D. (2003), An Introduction to the Theory of Point Processes, Volume I: Elementary Theory and Methods, 2nd edn., Springer.Google Scholar
Daley, D. J. & Vere-Jones, D. (2008), An Introduction to the Theory of Point Processes, Volume II: General Theory and Structure, 2nd edn., Springer.CrossRefGoogle Scholar
Dhillon, H. S., Ganti, R. K., Baccelli, F. & Andrews, J. G. (2012), Modeling and analysis of K-tier downlink heterogeneous cellular networks, IEEE Journal on Selected Areas in Communications 30(3), 550–560.CrossRefGoogle Scholar
Dousse, O., Franceschetti, M., Macris, N., Meester, R. & Thiran, P. (2006), Percolation in the signal-to-interference ratio graph, Journal of Applied Probability 43(2), 552–562.CrossRefGoogle Scholar
Durrett, R. (1985), Some general results concerning the critical exponents of percolation, Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete 69, 421–437.CrossRefGoogle Scholar
Fekete, M. (1923), Über die Verteilung der Wurzeln bei gewissen algebraischen Gleichungen mit ganzzahigen Koeffizienten, Mathematische Zeitschrift 17(1), 228–249.CrossRefGoogle Scholar
Fortuin, C. M., Kasteleyn, P. W. & Ginibre, J. (1971), Correlation inequalities on some partially ordered sets, Communications in Mathematical Physics 22(2), 89–103.CrossRefGoogle Scholar
Franceschetti, M. & Meester, R. (2007), Random Networks for Communication: From Statistical Physics to Information Systems, Cambridge University Press.Google Scholar
Franceschetti, M., Booth, L., Cook, M., Bruck, J. & Meester, R. (2005), Continuum percolation with unreliable and spread out connections, Journal of Statistical Physics 118(3/4), 721–734.CrossRefGoogle Scholar
Ganti, R. K. & Haenggi, M. (2007), Dynamic connectivity and packet propagation delay in ALOHA wireless networks, in 41st Asilomar Conference on Signals, Systems, and Computers (Asilomar '07), Pacific Grove, CA.Google Scholar
Ganti, R. K. & Haenggi, M. (2009a), Interference and outage in clustered wireless ad hoc networks, IEEE Transactions on Information Theory 55(9), 4067–4086.CrossRefGoogle Scholar
Ganti, R. K. & Haenggi, M. (2009b), Spatial and temporal correlation of the interference in ALOHA ad hoc networks, IEEE Communications Letters 13(9), 631–633.CrossRefGoogle Scholar
Ganti, R. K. & Haenggi, M. (2012), Dynamic connectivity and path formation time in Poisson networks, The Journal of Mobile Communication, Computation and Information, http://www.nd.edu/~mhaenggi/pubs/winet12.pdf.Google Scholar
Ganti, R. K., Andrews, J. G. & Haenggi, M. (2011), High-SIR transmission capacity of wireless networks with general fading and node distribution, IEEE Transactions on Information Theory 57(5), 3100–3116.CrossRefGoogle Scholar
Georgii, H.-O. (1976), Canonical and grand canonical Gibbs states for continuum systems, Communications in Mathematical Physics 48(1), 31–51.CrossRefGoogle Scholar
Giacomelli, R., Ganti, R. K. & Haenggi, M. (2011), Outage probability of general ad hoc networks in the high-reliability regime, IEEE/ACM Transactions on Networking 19(4), 1151–1163.CrossRefGoogle Scholar
Grandell, J. (1976), Doubly Stochastic Poisson Processes, Springer.CrossRefGoogle Scholar
Grimmett, G. (1999), Percolation, 2nd edn., Springer.CrossRefGoogle Scholar
Haenggi, M. (2008a), A geometric interpretation of fading in wireless networks: theory and applications, IEEE Transactions on Information Theory 54(12), 5500–5510.CrossRefGoogle Scholar
Haenggi, M. (2008b), The secrecy graph and some of its properties, in 2008 IEEE International Symposium on Information Theory (ISIT '08), Toronto.Google Scholar
Haenggi, M. (2009), Outage, local throughput, and capacity of random wireless networks, IEEE Transactions on Wireless Communications 8(8), 4350–4359.CrossRefGoogle Scholar
Haenggi, M. (2011), Mean interference in hard-core wireless networks, IEEE Communications Letters 15(8), 792–794.CrossRefGoogle Scholar
Haenggi, M. & Ganti, R. K. (2008), Interference in Large Wireless Networks, NOW.Google Scholar
Hall, P. (1985), On the coverage of k-dimensional space by k-dimensional spheres, The Annals of Probability 13(3), 991–1002.CrossRefGoogle Scholar
Harris, T. E. (1960), A lower bound on the critical probability in a certain percolation process, Mathematical Proceedings of the Cambridge Philosophical Society 56, 13–20.CrossRefGoogle Scholar
Heinrich, L. & Schmidt, V. (1985), Normal convergence of multidimensional shot noise and rates of this convergence, Advances in Applied Probability 17(4), 709–730.CrossRefGoogle Scholar
Illian, J., Penttinen, A., Stoyan, H. & Stoyan, D. (2008), Statistical Analysis and Modeling of Spatial Point Patterns, Wiley.Google Scholar
Ilow, J. & Hatzinakos, D. (1998), Analytical alpha-stable noise modeling in a Poisson field of interferers or scatterers, IEEE Transactions on Signal Processing 46(6), 1601–1611.CrossRefGoogle Scholar
Isham, V. (1984), Multitype Markov point processes: some approximations, Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences 391, 39–53.Google Scholar
Jacobsen, M. (2006), Point Process Theory and Applications: Marked Point and Piecewise Deterministic Processes, Birkhäuser.Google Scholar
Janson, S., Luczak, T. & Rucinski, A. (2000), Random Graphs, Wiley-Interscience.CrossRefGoogle Scholar
Kesten, H. (1980), The critical probability of bond percolation on the square lattice equals 1/2, Communications in Mathematical Physics 74(1), 41–59.CrossRefGoogle Scholar
Kingman, J. F. C. (1978), Uses of exchangeability, The Annals of Probability 6(2), 183–197.CrossRefGoogle Scholar
Kingman, J. F. C. (1993), Poisson Processes, Oxford Science Publications.Google Scholar
Lee, C.-H. & Haenggi, M. (2012), Interference and outage in Poisson cognitive networks, IEEE Transactions on Wireless Communications 11(4), 1392–1401.CrossRefGoogle Scholar
Lindvall, T. (2002), Lectures on the Coupling Method, Dover Publications.Google Scholar
Linnartz, J.-P. M. G. (1992), Exact analysis of the outage probability in multiple-user radio, IEEE Transactions on Communications 40(1), 20–23.CrossRefGoogle Scholar
Lowen, S. B. & Teich, M. C. (1990), Power-law shot noise, IEEE Transactions on Information Theory 36(6), 1302–1318.CrossRefGoogle Scholar
Matérn, B. (1986), Spatial Variation, 2nd edn., Springer.CrossRefGoogle Scholar
Mathai, A. M. (1999), An Introduction to Geometrical Probability, Gordon and Breach Science Publishers.Google Scholar
Mathar, R. & Mattfeldt, J. (1995), On the distribution of cumulated interference power in Rayleigh fading channels, Wireless Networks 1(1), 31–36.CrossRefGoogle Scholar
Matthes, K., Kerstan, J. & Mecke, J. (1978), Infinitely Divisible Point Processes, John Wiley & Sons.Google Scholar
Meester, R. & Roy, R. (1996), Continuum Percolation, Cambridge University Press.CrossRefGoogle Scholar
Musa, S. & Wasylkiwskyj, W. (1978), Co-channel interference of spread spectrum systems in a multiple user environment, IEEE Transactions on Communications 26(10), 1405–1413.CrossRefGoogle Scholar
Newman, D. S. (1970), A new family of point processes which are characterized by their second moment properties, Journal of Applied Probability 7(2), 338–358.CrossRefGoogle Scholar
Newman, M. E. J. & Ziff, R. M. (2000), Fast Monte Carlo algorithm for site or bond percolation, Physical Review Letters 85(19), 4104–4107.Google Scholar
Neyman, J. & Scott, E. L. (1952), A theory of the spatial distribution of galaxies, Astrophysical Journal 116, 144–163.CrossRefGoogle Scholar
Neyman, J. & Scott, E. L. (1958), Statistical approach to problems of cosmology, Journal of the Royal Statistical Society, SeriesB 20(1), 1–43.Google Scholar
Nguyen, X. X. & Zessin, H. (1979), Integral and differential characterization of the Gibbs process, Mathematische Nachrichten 88, 105–115.Google Scholar
Peierls, R. (1936), On Ising's model of ferromagnetism, Mathematical Proceedings of the Cambridge Philosophical Society 32, 477–481.CrossRefGoogle Scholar
Penrose, M. (2003), Random Geometric Graphs, Oxford University Press.CrossRefGoogle Scholar
Rényi, A. (1967), Remarks on the Poisson process, Studia Scientifica Mathematica Hungarica 2, 119–123.Google Scholar
Rice, S. O. (1944), Mathematical analysis of random noise, Bell System Technical Journal 23, 282–332.CrossRefGoogle Scholar
Ripley, B. D. (1976), The second-order analysis of stationary point processes, Journal of Applied Probability 13, 255–266.CrossRefGoogle Scholar
Samorodnitsky, G. & Taqqu, M. S. (1994), Stable Non-Gaussian Random Processes: Stochastic Models with Infinite Variance, Chapman & Hall.Google Scholar
Sarkar, A. & Haenggi, M. (2011), Percolation in the secrecy graph. ArXiv, http://arxiv.org/abs/1107.4613.
Sarkar, A. & Haenggi, M. (2012), Secrecy coverage, Internet Mathematics. Available at http://www.nd.edu/~mhaenggi/pubs/im12.pdf.Google Scholar
Schottky, W. (1918), Über spontane Stromschwankungen in verschiedenen Elektrizitätsleitern, Annalen der Physik 57, 541–567.Google Scholar
Sousa, E. S. (1990), Interference modeling in a direct-sequence spread-spectrum packet radio network, IEEE Transactions on Communications 38(9), 1475–1482.CrossRefGoogle Scholar
Sousa, E. S. & Silvester, J. A. (1990), Optimum transmission ranges in a direct-sequence spread-spectrum multihop packet radio network, IEEE Journal on Selected Areas in Communications 8(5), 762–771.CrossRefGoogle Scholar
Spencer, J. (2001), The Strange Logic of Random Graphs, Springer.CrossRefGoogle Scholar
Srinivasa, S. & Haenggi, M. (2010), Distance distributions in finite uniformly random networks: theory and applications, IEEE Transactions on Vehicular Technology 59(2), 940–949.CrossRefGoogle Scholar
Stoyan, D., Kendall, W. S. & Mecke, J. (1995), Stochastic Geometry and its Applications, 2nd edn., John Wiley & Sons.Google Scholar
Takagi, H. & Kleinrock, L. (1984), Optimal transmission ranges for randomly distributed packet radio terminals, IEEE Transactions on Communications 32(3), 246–257.CrossRefGoogle Scholar
van Lieshout, M. N. M. (2000), Markov Point Processes and their Applications, Imperial College Press.CrossRefGoogle Scholar
van Lieshout, M. N. M. (2011), A J-function for inhomogeneous point processes, Statistica Neerlandica 65(2), 183–201.CrossRefGoogle Scholar
van Lieshout, M. N. M. & Baddeley, A. J. (1996), A nonparametric measure of spatial interaction in point patterns, Statistica Neerlandica 50(3), 344–361.Google Scholar
Walters, M. (2012), Small components in k-nearest neighbour graphs, Discrete Applied Mathematics.Google Scholar
Weber, S. & Andrews, J. G. (2012), Transmission Capacity of Wireless Networks, NOW.Google Scholar
Weber, S., Yang, X., Andrews, J. G. & de Veciana, G. (2005), Transmission capacity of wireless ad hoc networks with outage constraints, IEEE Transactions on Information Theory 51(12), 4091–4102.CrossRefGoogle Scholar
Westcott, M. (1972), The probability generating functional, Journal of the Australian Mathematical Society 14, 448–466.CrossRefGoogle Scholar
Zorzi, M. & Pupolin, S. (1995), Optimum transmission ranges in multihop packet radio networks in the presence of fading, IEEE Transactions on Communications 43(7), 2201–2205.CrossRefGoogle Scholar

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

  • References
  • Martin Haenggi, University of Notre Dame, Indiana
  • Book: Stochastic Geometry for Wireless Networks
  • Online publication: 05 November 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9781139043816.016
Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

  • References
  • Martin Haenggi, University of Notre Dame, Indiana
  • Book: Stochastic Geometry for Wireless Networks
  • Online publication: 05 November 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9781139043816.016
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • References
  • Martin Haenggi, University of Notre Dame, Indiana
  • Book: Stochastic Geometry for Wireless Networks
  • Online publication: 05 November 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9781139043816.016
Available formats
×