메뉴 건너뛰기




Volumn 13, Issue 1, 2003, Pages 277-303

Weak laws of large numbers in geometric probability

Author keywords

Boolean model; Computational geometry; Minimal spanning tree; Nearest neighbors graph; Objective method; Proximity graph; Sphere of influence graph; Voronoi graph; Weak law of large numbers

Indexed keywords


EID: 0037274513     PISSN: 10505164     EISSN: None     Source Type: Journal    
DOI: 10.1214/aoap/1042765669     Document Type: Article
Times cited : (161)

References (30)
  • 1
    • 0001455013 scopus 로고
    • Asymptotics for Euclidean minimal spanning trees on random points
    • ALDOUS, D. and STEHLE, J. M. (1992). Asymptotics for Euclidean minimal spanning trees on random points. Probab. Theory Related Fields 92 247-258.
    • (1992) Probab. Theory Related Fields , vol.92 , pp. 247-258
    • Aldous, D.1    Stehle, J.M.2
  • 2
    • 21844510142 scopus 로고
    • Simultaneous uniqueness of infinite clusters in stationary random labeled graphs
    • Alexander, K. S. (1995). Simultaneous uniqueness of infinite clusters in stationary random labeled graphs. Comm. Math. Phys. 168 39-55.
    • (1995) Comm. Math. Phys. , vol.168 , pp. 39-55
    • Alexander, K.S.1
  • 5
    • 0036246763 scopus 로고    scopus 로고
    • Graph theoretic procedures for dimension identification
    • BRITO, M., QUIROZ, A. and YUKICH, J. E. (2002). Graph theoretic procedures for dimension identification. J. Multivariate Anal. 81 67-84.
    • (2002) J. Multivariate Anal. , vol.81 , pp. 67-84
    • Brito, M.1    Quiroz, A.2    Yukich, J.E.3
  • 6
    • 38249032698 scopus 로고
    • The expected size of some graphs in computational geometry
    • DEVROYE, L. (1988). The expected size of some graphs in computational geometry. Comput. Math. Appl. 15 53-64.
    • (1988) Comput. Math. Appl. , vol.15 , pp. 53-64
    • Devroye, L.1
  • 8
    • 26544478772 scopus 로고    scopus 로고
    • The expected size of a random sphere of influence graph
    • I. Bárány and K. Böröczky, eds. János Bolyai Math. Society, Budapest, Hungary
    • FÜREDI, Z. (1997). The expected size of a random sphere of influence graph. In Intuitive Geometry (I. Bárány and K. Böröczky, eds.) 319-326. János Bolyai Math. Society, Budapest, Hungary.
    • (1997) Intuitive Geometry , pp. 319-326
    • Füredi, Z.1
  • 9
  • 11
    • 0003049048 scopus 로고    scopus 로고
    • The proportion of triangles in a Poisson-Voronoi tessellation of the plane
    • HAYEN, A. and QUINE, M. P. (2000). The proportion of triangles in a Poisson-Voronoi tessellation of the plane. Adv. in Appl. Probab. 32 67-74.
    • (2000) Adv. in Appl. Probab. , vol.32 , pp. 67-74
    • Hayen, A.1    Quine, M.P.2
  • 12
    • 0001699274 scopus 로고
    • On the fraction of random points with specified nearest neighbor interrelations and degree of attraction
    • HENZE, N. (1987). On the fraction of random points with specified nearest neighbor interrelations and degree of attraction. Adv. in Appl. Probab. 19 873-895.
    • (1987) Adv. in Appl. Probab. , vol.19 , pp. 873-895
    • Henze, N.1
  • 14
    • 0026924875 scopus 로고
    • Relative neighborhood graphs and their relatives
    • JAROMCZYK, J. W. and TOUSSAINT, G. T. (1992). Relative neighborhood graphs and their relatives. Proc. IEEE 80 1502-1517.
    • (1992) Proc. IEEE , vol.80 , pp. 1502-1517
    • Jaromczyk, J.W.1    Toussaint, G.T.2
  • 15
    • 0036473994 scopus 로고    scopus 로고
    • Strong laws for Euclidean graphs with general edge weights
    • JIMENEZ, R. and YUKICH, J. E. (2002). Strong laws for Euclidean graphs with general edge weights. Statist. Probab. Lett. 56 251-259.
    • (2002) Statist. Probab. Lett. , vol.56 , pp. 251-259
    • Jimenez, R.1    Yukich, J.E.2
  • 16
    • 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. Probab. 6 495-527.
    • (1996) Ann. Appl. Probab. , vol.6 , pp. 495-527
    • Kesten, H.1    Lee, S.2
  • 19
    • 0033210542 scopus 로고    scopus 로고
    • Asymptotics for Voronoi tessellations on random samples
    • McGIVNEY, K. and YUKICH, J. E. (1999). Asymptotics for Voronoi tessellations on random samples. Stochastic Process. Appl. 83 273-288.
    • (1999) Stochastic Process. Appl. , vol.83 , pp. 273-288
    • McGivney, K.1    Yukich, J.E.2
  • 21
    • 0030353886 scopus 로고    scopus 로고
    • The random minimal spanning tree in high dimensions
    • PENROSE, M. D. (1996). The random minimal spanning tree in high dimensions. Ann. Probab. 24 1903-1925.
    • (1996) Ann. Probab. , vol.24 , pp. 1903-1925
    • Penrose, M.D.1
  • 22
    • 0035531727 scopus 로고    scopus 로고
    • Random parking, sequential adsorption, and the jamming limit
    • PENROSE, M. D. (2001). Random parking, sequential adsorption, and the jamming limit. Comm. Math. Phys. 218 153-176.
    • (2001) Comm. Math. Phys. , vol.218 , pp. 153-176
    • Penrose, M.D.1
  • 23
    • 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. Probab. 11 1005-1041.
    • (2001) Ann. Appl. Probab. , vol.11 , pp. 1005-1041
    • Penrose, M.D.1    Yukich, J.E.2
  • 24
    • 0036117358 scopus 로고    scopus 로고
    • Limit theory for random sequential packing and deposition
    • PENROSE, M. D. and YUKICH, J. E. (2001). Limit theory for random sequential packing and deposition. Ann. Appl. Probab. 12 272-301.
    • (2001) Ann. Appl. Probab. , vol.12 , pp. 272-301
    • Penrose, M.D.1    Yukich, J.E.2
  • 28
    • 0000907076 scopus 로고
    • On the number of leaves of a Euclidean minimal spanning tree
    • STEELE, J. M., SHEPP, L. and EDDY, W. (1987). On the number of leaves of a Euclidean minimal spanning tree. J. Appl. Probab. 24 809-826.
    • (1987) J. Appl. Probab. , vol.24 , pp. 809-826
    • Steele, J.M.1    Shepp, L.2    Eddy, W.3
  • 30
    • 0008663251 scopus 로고    scopus 로고
    • Asymptotics for weighted minimal spanning trees on random points
    • YUKICH, J. E. (1999). Asymptotics for weighted minimal spanning trees on random points. Stochastic Process. Appl. 85 123-138.
    • (1999) Stochastic Process. Appl. , vol.85 , pp. 123-138
    • Yukich, J.E.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.