메뉴 건너뛰기




Volumn 17, Issue 1, 2007, Pages 305-359

The radial spanning tree of a poisson point process

Author keywords

Asymptotic shape; Directed spanning tree; Nearest neighbor graph; Poisson point process; Spanning trees

Indexed keywords


EID: 51049090390     PISSN: 10505164     EISSN: 10505164     Source Type: Journal    
DOI: 10.1214/105051606000000826     Document Type: Article
Times cited : (50)

References (30)
  • 1
    • 51049086284 scopus 로고    scopus 로고
    • ALDOUS, D. and STEELE, M. (2004). The objective method: Probabilistic combinatorial optimization and local weak convergence. In Probability on Discrete Structures. Encyclopedia Math. Sci. 110 1-72. Springer, Berlin. MR2023650
    • ALDOUS, D. and STEELE, M. (2004). The objective method: Probabilistic combinatorial optimization and local weak convergence. In Probability on Discrete Structures. Encyclopedia Math. Sci. 110 1-72. Springer, Berlin. MR2023650
  • 2
    • 0002217156 scopus 로고
    • Percolation and minimal spanning trees in infinite graphs
    • MR1330762
    • ALEXANDER, K. (1995). Percolation and minimal spanning trees in infinite graphs. Ann. Probab. 23 87-104. MR1330762
    • (1995) Ann. Probab , vol.23 , pp. 87-104
    • ALEXANDER, K.1
  • 3
    • 0000991156 scopus 로고
    • A new approach to the limit theory of recurrent Markov chains
    • MR0511425
    • ATHREYA, K. and NEY, P. (1978). A new approach to the limit theory of recurrent Markov chains. Trans. Amer. Math. Soc. 245 493-501. MR0511425
    • (1978) Trans. Amer. Math. Soc , vol.245 , pp. 493-501
    • ATHREYA, K.1    NEY, P.2
  • 4
    • 51049105852 scopus 로고    scopus 로고
    • BACCELLI, F. and BRÉMAUD, P. (2003). Elements of Queuing Theory, 2nd ed. Springer, Berlin. MR1957884
    • BACCELLI, F. and BRÉMAUD, P. (2003). Elements of Queuing Theory, 2nd ed. Springer, Berlin. MR1957884
  • 5
    • 0032674407 scopus 로고    scopus 로고
    • Self organizing hierarchical multi-cast trees and their optimization
    • BACCELLI, F., KOFMAN, D. and ROUGIER, J. L. (1999). Self organizing hierarchical multi-cast trees and their optimization. In Proceedings of IEEE Infocom 3 1081-1089.
    • (1999) Proceedings of IEEE Infocom , vol.3 , pp. 1081-1089
    • BACCELLI, F.1    KOFMAN, D.2    ROUGIER, J.L.3
  • 6
    • 1842457648 scopus 로고    scopus 로고
    • On a random directed spanning tree
    • MR2035772
    • BHATT, A. and ROY, R. (2004). On a random directed spanning tree. Adv. in Appl. Probab. 36 19-42. MR2035772
    • (2004) Adv. in Appl. Probab , vol.36 , pp. 19-42
    • BHATT, A.1    ROY, R.2
  • 7
    • 51049121479 scopus 로고    scopus 로고
    • Navigation on a Poisson point process
    • Rapport INRIA 5790. Available at
    • BORDENAVE, C. (2006). Navigation on a Poisson point process. Rapport INRIA 5790. Available at http://arxiv.org/abs/math.PR/0601122.
    • (2006)
    • BORDENAVE, C.1
  • 8
    • 51049122040 scopus 로고    scopus 로고
    • DALEY, D. and VERE-JONES, D. (1988). An Introduction to the Theory of Point Processes. Springer, New York. MR0950166
    • DALEY, D. and VERE-JONES, D. (1988). An Introduction to the Theory of Point Processes. Springer, New York. MR0950166
  • 9
    • 51049088502 scopus 로고    scopus 로고
    • DEMBO, A. and ZEITOUNI, O. (1998). Large Deviations Techniques and Applications. Springer, New York. MR1619036
    • DEMBO, A. and ZEITOUNI, O. (1998). Large Deviations Techniques and Applications. Springer, New York. MR1619036
  • 11
    • 51049115650 scopus 로고    scopus 로고
    • FELLER, W. (1971). An Introduction to Probability Theory and Its Applications II, 2nd ed. Wiley, New York. MR0270403
    • FELLER, W. (1971). An Introduction to Probability Theory and Its Applications II, 2nd ed. Wiley, New York. MR0270403
  • 13
    • 23944487451 scopus 로고    scopus 로고
    • Two-dimensional Poisson trees converge to the Brownian web
    • MR2165253
    • FERRARI, P., FONTES, L. R. and WU, X.-Y. (2005). Two-dimensional Poisson trees converge to the Brownian web. Ann. Inst. H Poincarê Probab. Statist. 41 851-858. MR2165253
    • (2005) Ann. Inst. H Poincarê Probab. Statist , vol.41 , pp. 851-858
    • FERRARI, P.1    FONTES, L.R.2    WU, X.-Y.3
  • 14
    • 8744310229 scopus 로고    scopus 로고
    • The Brownian web: Characterization and convergence
    • MR2094432
    • FONTES, L., ISOPI, M., NEWMAN, C. and RAVISHANKAR, K. (2004). The Brownian web: Characterization and convergence. Ann. Probab. 32 2857-2883. MR2094432
    • (2004) Ann. Probab , vol.32 , pp. 2857-2883
    • FONTES, L.1    ISOPI, M.2    NEWMAN, C.3    RAVISHANKAR, K.4
  • 15
    • 8744309530 scopus 로고    scopus 로고
    • Random oriented trees: A model of drainage networks
    • MR2071422
    • GANGOPADHYAY, S., ROY, R. and SARKAR, A. (2004). Random oriented trees: A model of drainage networks. Ann. Appl. Probab. 14 1242-1266. MR2071422
    • (2004) Ann. Appl. Probab , vol.14 , pp. 1242-1266
    • GANGOPADHYAY, S.1    ROY, R.2    SARKAR, A.3
  • 16
    • 0002738510 scopus 로고
    • Convergence rates for probabilities of moderate deviations for sums of random. variables with multidimensional indices
    • MR0566595
    • GUT, A. (1980). Convergence rates for probabilities of moderate deviations for sums of random. variables with multidimensional indices. Ann. Probab. 8 298-313. MR0566595
    • (1980) Ann. Probab , vol.8 , pp. 298-313
    • GUT, A.1
  • 17
    • 0035537282 scopus 로고    scopus 로고
    • Geodesics and spanning trees for Euclidean first-passage percolation
    • MR1849171
    • HOWARD, C. and NEWMAN, C. (2001). Geodesics and spanning trees for Euclidean first-passage percolation. Ann. Probab. 29 577-623. MR1849171
    • (2001) Ann. Probab , vol.29 , pp. 577-623
    • HOWARD, C.1    NEWMAN, C.2
  • 18
    • 0031260688 scopus 로고    scopus 로고
    • The central limit theorem for Euclidian minimal spanning trees
    • MR1484795
    • LEE, S. (1997). The central limit theorem for Euclidian minimal spanning trees. Ann. Appl. Probab. 7 996-1020. MR1484795
    • (1997) Ann. Appl. Probab , vol.7 , pp. 996-1020
    • LEE, S.1
  • 19
    • 51049111071 scopus 로고    scopus 로고
    • MEYN, S. and TWEEDIE, R. (1993). Markov Chains and Stochastic Stability. Springer, Berlin. MR1287609
    • MEYN, S. and TWEEDIE, R. (1993). Markov Chains and Stochastic Stability. Springer, Berlin. MR1287609
  • 20
    • 51049087172 scopus 로고    scopus 로고
    • PENROSE, M. (2003). Random Geometric Graphs. Oxford Univ. Press. MR1986198
    • PENROSE, M. (2003). Random Geometric Graphs. Oxford Univ. Press. MR1986198
  • 21
    • 7544224726 scopus 로고    scopus 로고
    • Random minimal directed spanning trees and Dickman-type distributions
    • MR2079909
    • PENROSE, M. and WADE, A. (2004). Random minimal directed spanning trees and Dickman-type distributions. Adv. in Appl. Probab. 36 691-714. MR2079909
    • (2004) Adv. in Appl. Probab , vol.36 , pp. 691-714
    • PENROSE, M.1    WADE, A.2
  • 22
    • 33745946243 scopus 로고    scopus 로고
    • On the total length of the random minimal directed spanning tree
    • PENROSE, M. and WADE, A. (2006). On the total length of the random minimal directed spanning tree. Adv. in Appl. Probab. 38 336-372.
    • (2006) Adv. in Appl. Probab , vol.38 , pp. 336-372
    • PENROSE, M.1    WADE, A.2
  • 23
    • 0036117358 scopus 로고    scopus 로고
    • Limit theory for random sequential packing and deposition
    • MR1890065
    • PENROSE, M. and YUKICH, J. (2001). Limit theory for random sequential packing and deposition. Ann. Appl. Probab. 12 272-301. MR1890065
    • (2001) Ann. Appl. Probab , vol.12 , pp. 272-301
    • PENROSE, M.1    YUKICH, J.2
  • 24
    • 0037274513 scopus 로고    scopus 로고
    • Weak laws of large numbers in geometric probability
    • MR1952000
    • PENROSE, M. and YUKICH, J. (2003). Weak laws of large numbers in geometric probability. Ann. Appl. Probab. 13 277-303. MR1952000
    • (2003) Ann. Appl. Probab , vol.13 , pp. 277-303
    • PENROSE, M.1    YUKICH, J.2
  • 25
    • 0001213874 scopus 로고
    • A matching problem and subadditive Euclidean functionals
    • MR1233626
    • RHEE, W. (1993). A matching problem and subadditive Euclidean functionals. Ann. Appl. Probab. 3 794-801. MR1233626
    • (1993) Ann. Appl. Probab , vol.3 , pp. 794-801
    • RHEE, W.1
  • 26
    • 51049105626 scopus 로고    scopus 로고
    • STEELE, J. M. (1988). Growth rates of Euclidean minimal spanning trees with power weighted edges. Ann. Probab. 16 1767-1787. MR0958215
    • STEELE, J. M. (1988). Growth rates of Euclidean minimal spanning trees with power weighted edges. Ann. Probab. 16 1767-1787. MR0958215
  • 28
    • 51249165477 scopus 로고
    • Concentration of measure and isoperimetric inequalities in product spaces
    • MR1361756
    • TALAGRAND, M. (1995). Concentration of measure and isoperimetric inequalities in product spaces. Inst. Hautes Études Sci. Publ. Math. 81 73-205. MR1361756
    • (1995) Inst. Hautes Études Sci. Publ. Math , vol.81 , pp. 73-205
    • TALAGRAND, M.1
  • 29
    • 0041414614 scopus 로고    scopus 로고
    • The true self repelling motion
    • MR1640799
    • TOTH, B. and WERNER, W. (1998). The true self repelling motion. Probab. Theory Related Fields 111 375-452. MR1640799
    • (1998) Probab. Theory Related Fields , vol.111 , pp. 375-452
    • TOTH, B.1    WERNER, W.2
  • 30
    • 51049098231 scopus 로고    scopus 로고
    • YUKICH, J. (1998). Probability Theory of Classical Euclidean Optimization Problems. Springer, Berlin. MR1632875
    • YUKICH, J. (1998). Probability Theory of Classical Euclidean Optimization Problems. Springer, Berlin. MR1632875


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.