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Volumn , Issue , 2008, Pages 1-196

Random networks for communication: From statistical physics to information systems

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EID: 84926098135     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1017/CBO9780511619632     Document Type: Book
Times cited : (156)

References (92)
  • 2
    • 0001607449 scopus 로고
    • Uniqueness of the infinite cluster and continuity of connectivity functions for short- and log-range percolation
    • Aizenman, M., H. Kesten, C. Newman (1987). Uniqueness of the infinite cluster and continuity of connectivity functions for short- and log-range percolation. Communications in Mathematical Physics 111, 505-32.
    • (1987) Communications in Mathematical Physics , vol.111 , pp. 505-532
    • Aizenman, M.1    Kesten, H.2    Newman, C.3
  • 3
    • 21344480033 scopus 로고
    • Finite clusters in high density continuum percolation: Compression and sphericality
    • Alexander, K. (1991). Finite clusters in high density continuum percolation: compression and sphericality. Probability Theory and Related Fields 97, 35-63.
    • (1991) Probability Theory and Related Fields , vol.97 , pp. 35-63
    • Alexander, K.1
  • 5
    • 0030522185 scopus 로고    scopus 로고
    • On the chemical distance for supercritical Bernoulli percolation
    • Antal, P., A. Pisztora (1996). On the chemical distance for supercritical Bernoulli percolation. Annals of Probability 24(2), 1036-48.
    • (1996) Annals of Probability , vol.24 , Issue.2 , pp. 1036-1048
    • Antal, P.1    Pisztora, A.2
  • 6
    • 0002005293 scopus 로고
    • Two moments suffice for Poisson approximations: The Chen-Stein method
    • Arratia, R., L. Goldstein, L. Gordon (1989). Two moments suffice for Poisson approximations: the Chen-Stein method. Annals of Probability 17(1), 9-25.
    • (1989) Annals of Probability , vol.17 , Issue.1 , pp. 9-25
    • Arratia, R.1    Goldstein, L.2    Gordon, L.3
  • 11
    • 0022116584 scopus 로고
    • Inequalities with applications to percolation and reliability
    • Berg, van den, R., H. Kesten (1985). Inequalities with applications to percolation and reliability. Journal of Applied Probability 22, 556-69.
    • (1985) Journal of Applied Probability , vol.22 , pp. 556-569
    • Berg van den, R.1    Kesten, H.2
  • 12
    • 11944253901 scopus 로고    scopus 로고
    • Cambridge: Cambridge University Press
    • Bollobás, B. (2001). Random Graphs. Cambridge: Cambridge University Press.
    • (2001) Random Graphs
    • Bollobás, B.1
  • 14
    • 34547197519 scopus 로고    scopus 로고
    • Cambridge: Cambridge University Press
    • Bollobás, B., O. Riordan (2006). Percolation. Cambridge: Cambridge University Press.
    • (2006) Percolation
    • Bollobás, B.1    Riordan, O.2
  • 15
    • 21144445765 scopus 로고    scopus 로고
    • Covering algorithms, continuum percolation, and the geometry of wireless networks
    • Booth, L., J. Bruck, M. Franceschetti, R. Meester (2003). Covering algorithms, continuum percolation, and the geometry of wireless networks. Annals of Applied Probability 13(2), 722-31.
    • (2003) Annals of Applied Probability , vol.13 , Issue.2 , pp. 722-731
    • Booth, L.1    Bruck, J.2    Franceschetti, M.3    Meester, R.4
  • 19
    • 34547143925 scopus 로고    scopus 로고
    • Critical percolation exploration path and SLE6: A proof of convergence
    • press
    • Camia, F., C. Newman (2007). Critical percolation exploration path and SLE6: a proof of convergence. Probability Theory and Related Fields. In press.
    • (2007) Probability Theory and Related Fields
    • Camia, F.1    Newman, C.2
  • 20
    • 0001067389 scopus 로고
    • Poisson approximation for dependent trials
    • Chen, L. H. Y. (1975). Poisson approximation for dependent trials. Annals of Probability 3, 534-45.
    • (1975) Annals of Probability , vol.3 , pp. 534-545
    • Chen, L.H.Y.1
  • 23
  • 26
  • 29
    • 84929729015 scopus 로고    scopus 로고
    • Cambridge: Cambridge University Press
    • Durrett, R. (2007). Random Graph Dynamics. Cambridge: Cambridge University Press.
    • (2007) Random Graph Dynamics
    • Durrett, R.1
  • 34
    • 64549111723 scopus 로고    scopus 로고
    • A note on Lévéque and Telatar’s upper bound on the capacity of wireless ad-hoc networks
    • Franceschetti, M. (2007). A note on Lévéque and Telatar’s upper bound on the capacity of wireless ad-hoc networks. IEEE Transactions on Information Theory 53(9), 3207-11.
    • (2007) IEEE Transactions on Information Theory , vol.53 , Issue.9 , pp. 3207-3211
    • Franceschetti, M.1
  • 37
    • 33745173440 scopus 로고    scopus 로고
    • Critical node lifetimes in random networks via the Chen-Stein method
    • Franceschetti, M., R. Meester (2006a). Critical node lifetimes in random networks via the Chen-Stein method. IEEE Transactions on Information Theory 52(6), 2831-7.
    • (2006) IEEE Transactions on Information Theory , vol.52 , Issue.6 , pp. 2831-2837
    • Franceschetti, M.1    Meester, R.2
  • 38
    • 33947239726 scopus 로고    scopus 로고
    • Navigation in small world networks, a continuum, scale-free model
    • Franceschetti, M., R. Meester (2006b). Navigation in small world networks, a continuum, scale-free model. Journal of Applied Probability 43(4), 1173-80.
    • (2006) Journal of Applied Probability , vol.43 , Issue.4 , pp. 1173-1180
    • Franceschetti, M.1    Meester, R.2
  • 40
    • 34047145938 scopus 로고    scopus 로고
    • Efficient routing in Poisson small-world networks
    • Ganesh, A., M. Draief (2006). Efficient routing in Poisson small-world networks. Journal of Applied Probability 43(3), 678-86.
    • (2006) Journal of Applied Probability , vol.43 , Issue.3 , pp. 678-686
    • Ganesh, A.1    Draief, M.2
  • 41
    • 0000657887 scopus 로고
    • Random plane networks
    • Gilbert, E. N. (1961). Random plane networks. Journal of SIAM 9, 533-43.
    • (1961) Journal of SIAM , vol.9 , pp. 533-543
    • Gilbert, E.N.1
  • 42
    • 30844471744 scopus 로고    scopus 로고
    • Monotone properties of random geometric graphs have sharp thresholds
    • Goel, A., S. Rai, B. Krishnamachari (2005). Monotone properties of random geometric graphs have sharp thresholds. Annals of Applied Probability 15(4), 2535-52.
    • (2005) Annals of Applied Probability , vol.15 , Issue.4 , pp. 2535-2552
    • Goel, A.1    Rai, S.2    Krishnamachari, B.3
  • 43
    • 0037445514 scopus 로고    scopus 로고
    • A clustering procedure based on the comparison between the k nearest neighbors graph and the minimal spanning tree
    • Gonzáles-Barrios, J. M., A. J. Quiroz (2003). A clustering procedure based on the comparison between the k nearest neighbors graph and the minimal spanning tree. Statistics and Probability Letters 62, 23-34.
    • (2003) Statistics and Probability Letters , vol.62 , pp. 23-34
    • Gonzáles-Barrios, J.M.1    Quiroz, A.J.2
  • 44
    • 0004246476 scopus 로고    scopus 로고
    • Berlin: Springer Verlag
    • Grimmett, G. (1999). Percolation. Berlin: Springer Verlag.
    • (1999) Percolation
    • Grimmett, G.1
  • 45
    • 0032237818 scopus 로고    scopus 로고
    • Critical probabilities for site and bond percolation models
    • Grimmett, G., A. Stacey (1998). Critical probabilities for site and bond percolation models. Annals of Probability 26(4), 1788-1812.
    • (1998) Annals of Probability , vol.26 , Issue.4 , pp. 1788-1812
    • Grimmett, G.1    Stacey, A.2
  • 49
    • 0039056192 scopus 로고    scopus 로고
    • Nearest neighbor and hard sphere models in continuum percolation
    • Häggström, O., R. Meester (1996). Nearest neighbor and hard sphere models in continuum percolation. Random Structures and Algorithms 9(3), 295-315.
    • (1996) Random Structures and Algorithms , vol.9 , Issue.3 , pp. 295-315
    • Häggström, O.1    Meester, R.2
  • 50
    • 0002446794 scopus 로고
    • A lower bound on the critical probability of a certain percolation process
    • Harris, T. (1960). A lower bound on the critical probability of a certain percolation process. Proceedings of the Cambridge Philosophical Society 56, 13-20.
    • (1960) Proceedings of the Cambridge Philosophical Society , vol.56 , pp. 13-20
    • Harris, T.1
  • 53
    • 0002697969 scopus 로고
    • The critical probability of bond percolation on the square lattice equals 1/2
    • Kesten, H. (1980). The critical probability of bond percolation on the square lattice equals 1/2. Communications in Mathematical Physics 74, 41-59.
    • (1980) Communications in Mathematical Physics , vol.74 , pp. 41-59
    • Kesten, H.1
  • 57
    • 15044364840 scopus 로고    scopus 로고
    • Information theoretic upper bounds on the capacity of large extended ad hoc wireless networks
    • Lévêque, O., E. Telatar (2005). Information theoretic upper bounds on the capacity of large extended ad hoc wireless networks. IEEE Transactions on Information Theory 51(3), 858-65.
    • (2005) IEEE Transactions on Information Theory , vol.51 , Issue.3 , pp. 858-865
    • Lévêque, O.1    Telatar, E.2
  • 60
    • 0346846412 scopus 로고    scopus 로고
    • On central limit theorems in the random connection model
    • Meester, R., T. van de Brug (2004). On central limit theorems in the random connection model. Physica A 332, 263-78.
    • (2004) Physica A , vol.332 , pp. 263-278
    • Meester, R.1    van de Brug, T.2
  • 62
    • 0040865543 scopus 로고
    • Uniqueness of unbounded and vacant components in boolean models
    • Meester, R., R. Roy (1994). Uniqueness of unbounded and vacant components in boolean models. Advances in Applied Probability 4(3), 933-51.
    • (1994) Advances in Applied Probability , vol.4 , Issue.3 , pp. 933-951
    • Meester, R.1    Roy, R.2
  • 64
    • 85010248741 scopus 로고
    • Reliable circuits using less reliable relays I, II
    • Moore, E., C. Shannon (1956). Reliable circuits using less reliable relays I, II. Journal of the Franklin Institute 262, 191-208, 281-97.
    • (1956) Journal of the Franklin Institute , vol.262
    • Moore, E.1    Shannon, C.2
  • 65
    • 84980082497 scopus 로고
    • Certain factors affecting telegraph speed
    • Nyquist, H. (1924). Certain factors affecting telegraph speed. Bell Systems Technical Journal 3, 324.
    • (1924) Bell Systems Technical Journal , vol.3 , pp. 324
    • Nyquist, H.1
  • 66
    • 35148893949 scopus 로고    scopus 로고
    • Hierarchical cooperation achieves optimal capacity scaling in ad hoc networks
    • Özgür, A., O. Lévêque, D. Tse (2007). Hierarchical cooperation achieves optimal capacity scaling in ad hoc networks. IEEE Transactions on Information Theory, 53(10), 3549-72.
    • (2007) IEEE Transactions on Information Theory , vol.53 , Issue.10 , pp. 3549-3572
    • Özgür, A.1    Lévêque, O.2    Tse, D.3
  • 68
    • 0001012904 scopus 로고
    • On a continuum percolation model
    • Penrose, M. D. (1991). On a continuum percolation model. Advances in Applied Probability 23(3), 536-56.
    • (1991) Advances in Applied Probability , vol.23 , Issue.3 , pp. 536-556
    • Penrose, M.D.1
  • 69
    • 0000705654 scopus 로고
    • On the spread-out limit for bond and continuum percolation
    • Penrose, M. D. (1993). On the spread-out limit for bond and continuum percolation. Annals of Applied Probability 3(1), 253-76.
    • (1993) Annals of Applied Probability , vol.3 , Issue.1 , pp. 253-276
    • Penrose, M.D.1
  • 70
    • 0031287494 scopus 로고    scopus 로고
    • The longest edge of the random minimal spanning tree
    • Penrose, M. D. (1997). The longest edge of the random minimal spanning tree. Annals of Applied Probability 7(2), 340-61.
    • (1997) Annals of Applied Probability , vol.7 , Issue.2 , pp. 340-361
    • Penrose, M.D.1
  • 72
    • 0007262590 scopus 로고    scopus 로고
    • Large deviations for discrete and continuous percolation
    • Penrose, M. D., A. Pisztora (1996). Large deviations for discrete and continuous percolation. Advances in Applied Probability 28(1), 29-52.
    • (1996) Advances in Applied Probability , vol.28 , Issue.1 , pp. 29-52
    • Penrose, M.D.1    Pisztora, A.2
  • 73
    • 0037302672 scopus 로고    scopus 로고
    • High density asymptotics of the Poisson random connection model
    • Roy, R., A. Sarkar (2003). High density asymptotics of the Poisson random connection model. Physica A 318, 230-42.
    • (2003) Physica A , vol.318 , pp. 230-242
    • Roy, R.1    Sarkar, A.2
  • 78
    • 84856043672 scopus 로고
    • A mathematical theory of communication
    • Reprinted as: The Mathematical Theory of Communication. Champaign: University of Illinois Press
    • Shannon, C. (1948). A mathematical theory of communication. Bell Systems Technical Journal 27, 379-423, 623-56. Reprinted as: The Mathematical Theory of Communication. Champaign: University of Illinois Press.
    • (1948) Bell Systems Technical Journal , vol.27
    • Shannon, C.1
  • 79
    • 0041869040 scopus 로고    scopus 로고
    • Critical percolation in the plane: Conformal invariance, Cardy’s formula, scaling limits
    • Smirnov, S. (2001). Critical percolation in the plane: conformal invariance, Cardy’s formula, scaling limits. Les Comptes Rendus de l’Académie des Sciences, Série I, Mathematique 333(3), 239-44.
    • (2001) Les Comptes Rendus de l’Académie des Sciences, Série I, Mathematique , vol.333 , Issue.3 , pp. 239-244
    • Smirnov, S.1
  • 80
    • 0035527905 scopus 로고    scopus 로고
    • Critical exponents for two-dimensional percolation
    • Smirnov, S., W. Werner (2001). Critical exponents for two-dimensional percolation. Mathematical Research Letters 8, 729-44.
    • (2001) Mathematical Research Letters , vol.8 , pp. 729-744
    • Smirnov, S.1    Werner, W.2
  • 81
    • 0011001087 scopus 로고
    • Asymptotic evaluation of the number of latin rectangles
    • Stein, C. (1978). Asymptotic evaluation of the number of latin rectangles. Journal of Combinatorial Theory A 25, 38-49.
    • (1978) Journal of Combinatorial Theory A , vol.25 , pp. 38-49
    • Stein, C.1
  • 82
    • 0000055593 scopus 로고
    • On Russo’s approximate zero-one law
    • Talagrand, M. (1994). On Russo’s approximate zero-one law. Annals of Probability 22(3), 1576-87.
    • (1994) Annals of Probability , vol.22 , Issue.3 , pp. 1576-1587
    • Talagrand, M.1
  • 83
  • 85
    • 0032482432 scopus 로고    scopus 로고
    • Collective dynamics of small-world networks
    • Watts, D. J., S. H. Strogatz (1998). Collective dynamics of small-world networks. Nature 393, 440-2.
    • (1998) Nature , vol.393 , pp. 440-442
    • Watts, D.J.1    Strogatz, S.H.2
  • 87
    • 2442587377 scopus 로고    scopus 로고
    • A network information theory for wireless communication: Scaling laws and optimal operation
    • Xie, L. L., P. R. Kumar (2004). A network information theory for wireless communication: scaling laws and optimal operation. IEEE Transactions on Information Theory 50(5), 748-67.
    • (2004) IEEE Transactions on Information Theory , vol.50 , Issue.5 , pp. 748-767
    • Xie, L.L.1    Kumar, P.R.2
  • 88
    • 1042289031 scopus 로고    scopus 로고
    • The number of neighbors needed for connectivity of wireless networks
    • Xue, F., P. R. Kumar (2004). The number of neighbors needed for connectivity of wireless networks. Wireless Networks 10, 169-81.
    • (2004) Wireless Networks , vol.10 , pp. 169-181
    • Xue, F.1    Kumar, P.R.2
  • 89
    • 15044353953 scopus 로고    scopus 로고
    • The transport capacity of wireless networks over fading channels
    • Xue, F., L. L. Xie, P. R. Kumar (2005). The transport capacity of wireless networks over fading channels. IEEE Transactions on Information Theory, 51(3), 834-47.
    • (2005) IEEE Transactions on Information Theory , vol.51 , Issue.3 , pp. 834-847
    • Xue, F.1    Xie, L.L.2    Kumar, P.R.3
  • 90
    • 34047123679 scopus 로고    scopus 로고
    • Ultra-small scale-free geometric networks
    • Yukich, J. E. (2006). Ultra-small scale-free geometric networks. Journal of Applied Probability 43(3), 665-77.
    • (2006) Journal of Applied Probability , vol.43 , Issue.3 , pp. 665-677
    • Yukich, J.E.1
  • 91
    • 84926102273 scopus 로고
    • Proof of Lemma 11.12
    • G. Grimmett, (1999) Berlin: Springer Verlag
    • Zhang, Y. (1988). Proof of Lemma 11.12. In G. Grimmett (1999), Percolation. Berlin: Springer Verlag.
    • (1988) Percolation
    • Zhang, Y.1
  • 92
    • 0031986772 scopus 로고    scopus 로고
    • The kissing number of convex bodies. A brief survey
    • Zong, C. (1998). The kissing number of convex bodies. A brief survey. Bulletin of the London Mathematical Society 30(1), 1-10.
    • (1998) Bulletin of the London Mathematical Society , vol.30 , Issue.1 , pp. 1-10
    • Zong, C.1


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