메뉴 건너뛰기




Volumn 38, Issue 2, 2006, Pages 336-372

On the total length of the random minimal directed spanning tree

Author keywords

Fixed point equation; Fragmentation process; Nearest neighbour graph; Phase transition; Spanning tree; Weak convergence

Indexed keywords

ALGORITHMS; ASYMPTOTIC STABILITY; CONVERGENCE OF NUMERICAL METHODS; PHASE TRANSITIONS; PROBABILITY; TREES (MATHEMATICS);

EID: 33745946243     PISSN: 00018678     EISSN: None     Source Type: Journal    
DOI: 10.1239/aap/1151337075     Document Type: Article
Times cited : (23)

References (23)
  • 1
    • 33646119184 scopus 로고    scopus 로고
    • Rooted edges in a minimal directed spanning tree
    • Bai, Z.-D., Lee, S. and Penrose, M. D. (2006). Rooted edges in a minimal directed spanning tree. Adv. Appl. Prob. 38, 1-30.
    • (2006) Adv. Appl. Prob. , vol.38 , pp. 1-30
    • Bai, Z.-D.1    Lee, S.2    Penrose, M.D.3
  • 2
    • 0001034387 scopus 로고
    • On the distribution of the number of admissible points in a vector random sample
    • Barndorff-Nielsen O. and Sobel, M. (1966). On the distribution of the number of admissible points in a vector random sample. Theory Prob. Appl. 11, 249-269.
    • (1966) Theory Prob. Appl. , vol.11 , pp. 249-269
    • Barndorff-Nielsen, O.1    Sobel, M.2
  • 3
    • 4644316166 scopus 로고    scopus 로고
    • A symptotic laws for nonconservative selfsimilar fragmentations
    • Bertoin, J. and Gnedin, A. (2004). A symptotic laws for nonconservative selfsimilar fragmentations. Electron. J. Prob. 9, 575-593.
    • (2004) Electron. J. Prob. , vol.9 , pp. 575-593
    • Bertoin, J.1    Gnedin, A.2
  • 4
    • 35248850625 scopus 로고    scopus 로고
    • Degree distribution of the FKP model
    • (Proc. 30th Internat. Colloquium, ICALP 2003, Eindhoven; Lecture Notes Comp. Sci.), eds J. C. M. Baeten, J. K. Lenstra, J. Parrow and G. J. Woeginger, Springer, Berlin
    • Berger, N. et al. (2003). Degree distribution of the FKP model. In Automata, Languages and Programming (Proc. 30th Internat. Colloquium, ICALP 2003, Eindhoven; Lecture Notes Comp. Sci. 2719), eds J. C. M. Baeten, J. K. Lenstra, J. Parrow and G. J. Woeginger, Springer, Berlin, pp. 725-738.
    • (2003) Automata, Languages and Programming , vol.2719 , pp. 725-738
    • Berger, N.1
  • 5
    • 1842457648 scopus 로고    scopus 로고
    • On a random directed spanning tree
    • Bhatt, A. G. and Roy, R. (2004). On a random directed spanning tree. Adv. Appl. Prob. 36, 19-42.
    • (2004) Adv. Appl. Prob. , vol.36 , pp. 19-42
    • Bhatt, A.G.1    Roy, R.2
  • 7
    • 12744265111 scopus 로고    scopus 로고
    • Asymptotics of divide-and-conquer recurrences: Batcher's sorting algorithm and a minimum Euclidean matching heuristic
    • Hwang, H.-K. (1998). Asymptotics of divide-and-conquer recurrences: Batcher's sorting algorithm and a minimum Euclidean matching heuristic. Algorithmica 22, 529-546.
    • (1998) Algorithmica , vol.22 , pp. 529-546
    • Hwang, H.-K.1
  • 8
    • 0030501338 scopus 로고    scopus 로고
    • The central limit theorem for weighted minimal spanning trees on random points
    • Kesten, H. and Lee, S. (1996). The central limit theorem for weighted minimal spanning trees on random points. Ann. Appl. Prob. 6, 495-527.
    • (1996) Ann. Appl. Prob. , vol.6 , pp. 495-527
    • Kesten, H.1    Lee, S.2
  • 9
    • 0003523893 scopus 로고
    • (Oxford Stud. Prob.). Clarendon Press, Oxford
    • Kingman, J. F. C. (1993). Poisson Processes (Oxford Stud. Prob. 3). Clarendon Press, Oxford.
    • (1993) Poisson Processes , vol.3
    • Kingman, J.F.C.1
  • 10
    • 4544255498 scopus 로고    scopus 로고
    • A general limit theorem for recursive algorithms and combinatorial structures
    • Neininger, R. and Rüschendorf, L. (2004). A general limit theorem for recursive algorithms and combinatorial structures. Ann. Appl. Prob. 14, 378-418.
    • (2004) Ann. Appl. Prob. , vol.14 , pp. 378-418
    • Neininger, R.1    Rüschendorf, L.2
  • 11
    • 0012535670 scopus 로고    scopus 로고
    • (Oxford Stud. Prob.). Oxford University Press
    • Penrose, M. (2003). Random Geometric Graphs (Oxford Stud. Prob. 5). Oxford University Press.
    • (2003) Random Geometric Graphs , vol.5
    • Penrose, M.1
  • 12
    • 27644525072 scopus 로고    scopus 로고
    • Multivariate spatial central limit theorems with applications to percolation and spatial graphs
    • Penrose, M. D. (2005). Multivariate spatial central limit theorems with applications to percolation and spatial graphs. Ann. Prob. 33, 1945-1991.
    • (2005) Ann. Prob. , vol.33 , pp. 1945-1991
    • Penrose, M.D.1
  • 13
    • 7544238245 scopus 로고    scopus 로고
    • On the total length of the random minimal directed spanning tree
    • Preprint. Available at
    • Penrose, M. D. and Wade, A. R. (2004). On the total length of the random minimal directed spanning tree. Preprint. Available at http://arxiv.org/ abs/math.PR/0409201.
    • (2004)
    • Penrose, M.D.1    Wade, A.R.2
  • 14
    • 7544224726 scopus 로고    scopus 로고
    • Random minimal directed spanning trees and Dickman-type distributions
    • Penrose, M. D. and Wade, A. R. (2004). Random minimal directed spanning trees and Dickman-type distributions. Adv. Appl. Prob. 36, 691-714.
    • (2004) Adv. Appl. Prob. , vol.36 , pp. 691-714
    • Penrose, M.D.1    Wade, A.R.2
  • 15
    • 33745960315 scopus 로고    scopus 로고
    • Limit theory for the random on-line nearest-neighbour graph
    • Preprint. Available at
    • Penrose, M. D. and Wade, A. R. (2006). Limit theory for the random on-line nearest-neighbour graph. Preprint. Available at http://arxiv.org/ abs/math.PR/0603561.
    • (2006)
    • Penrose, M.D.1    Wade, A.R.2
  • 16
    • 0035497809 scopus 로고    scopus 로고
    • Central limit theorems for some graphs in computational geometry
    • Penrose, M. D. and Yukich, J. E. (2001). Central limit theorems for some graphs in computational geometry. Ann. Appl. Prob. 11, 1005-1041.
    • (2001) Ann. Appl. Prob. , vol.11 , pp. 1005-1041
    • Penrose, M.D.1    Yukich, J.E.2
  • 17
    • 0037274513 scopus 로고    scopus 로고
    • Weak laws of large numbers in geometric probability
    • Penrose, M. D. and Yukich, J. E. (2003). Weak laws of large numbers in geometric probability. Ann. Appl. Prob. 13, 277-303.
    • (2003) Ann. Appl. Prob. , vol.13 , pp. 277-303
    • Penrose, M.D.1    Yukich, J.E.2
  • 19
    • 38249008257 scopus 로고
    • A fixed point theorem for distributions
    • Rösler, U. (1992). A fixed point theorem for distributions. Stoch. Process. Appl. 42, 195-214.
    • (1992) Stoch. Process. Appl. , vol.42 , pp. 195-214
    • Rösler, U.1
  • 20
    • 0002015483 scopus 로고    scopus 로고
    • The contraction method for recursive algorithms
    • Rösler, U. and Rüschendorf, L. (2001). The contraction method for recursive algorithms. Algorithmica 29, 3-33.
    • (2001) Algorithmica , vol.29 , pp. 3-33
    • Rösler, U.1    Rüschendorf, L.2
  • 21
    • 0035633088 scopus 로고    scopus 로고
    • Large deviation principles for Euclidean functionals and other nearly additive processes
    • Seppäläinen, T. and Yukich, J. E. (2001). Large deviation principles for Euclidean functionals and other nearly additive processes. Prob. Theory Relat. Fields 120, 309-345.
    • (2001) Prob. Theory Relat. Fields , vol.120 , pp. 309-345
    • Seppäläinen, T.1    Yukich, J.E.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.