메뉴 건너뛰기




Volumn 36, Issue 3, 2004, Pages 667-690

Large Poisson-Voronoi cells and Crofton cells

Author keywords

Asymptotic shape; Crofton cell; D. G. Kendall's conjecture; Intrinsic volume; Poisson hyperplane tessellation; Poisson Voronoi tessellation; Typical cell

Indexed keywords

ESTIMATION; PROBABILITY; RANDOM PROCESSES; THEOREM PROVING;

EID: 7444234398     PISSN: 00018678     EISSN: None     Source Type: Journal    
DOI: 10.1239/aap/1093962228     Document Type: Article
Times cited : (34)

References (17)
  • 1
    • 0036955217 scopus 로고    scopus 로고
    • The distributions of the smallest disks containing the Poisson-Voronoi typical cell and the Crofton cell in the plane
    • Calka, P. (2002). The distributions of the smallest disks containing the Poisson-Voronoi typical cell and the Crofton cell in the plane. Adv. Appl. Prob. 34, 702-717.
    • (2002) Adv. Appl. Prob. , vol.34 , pp. 702-717
    • Calka, P.1
  • 2
    • 0002383112 scopus 로고    scopus 로고
    • Stability of inequalities in the dual Brunn-Minkowski theory
    • Gardner, R. J. and Vassallo, S. (1999). Stability of inequalities in the dual Brunn-Minkowski theory. J. Math. Anal. Appl. 231, 568-587.
    • (1999) J. Math. Anal. Appl. , vol.231 , pp. 568-587
    • Gardner, R.J.1    Vassallo, S.2
  • 3
    • 0032237131 scopus 로고    scopus 로고
    • Sur une conjecture de D. G. Kendall concernant la cellule de Crofton du plan et sur sa contrepartie brownienne
    • Goldman, A. (1998). Sur une conjecture de D. G. Kendall concernant la cellule de Crofton du plan et sur sa contrepartie brownienne. Ann. Prob. 26, 1727-1750.
    • (1998) Ann. Prob. , vol.26 , pp. 1727-1750
    • Goldman, A.1
  • 5
    • 0041304750 scopus 로고
    • Stability estimates for some geometric inequalities
    • Groemer, H. and Schneider, R. (1991). Stability estimates for some geometric inequalities. Bull. London Math. Soc. 23, 67-74.
    • (1991) Bull. London Math. Soc. , vol.23 , pp. 67-74
    • Groemer, H.1    Schneider, R.2
  • 6
    • 2942560334 scopus 로고    scopus 로고
    • Large cells in Poisson-Delaunay tessellations
    • Hug, D. and Schneider, R. (2004). Large cells in Poisson-Delaunay tessellations. Discrete Comput. Geom. 31, 503-514.
    • (2004) Discrete Comput. Geom. , vol.31 , pp. 503-514
    • Hug, D.1    Schneider, R.2
  • 7
    • 2142640516 scopus 로고    scopus 로고
    • The limit shape of the zero cell in a stationary Poisson hyperplane tessellation
    • Hug, D., Reitzner, M. and Schneider, R. (2004). The limit shape of the zero cell in a stationary Poisson hyperplane tessellation. Ann. Prob. 32, 1140-1167.
    • (2004) Ann. Prob. , vol.32 , pp. 1140-1167
    • Hug, D.1    Reitzner, M.2    Schneider, R.3
  • 8
    • 2142823730 scopus 로고    scopus 로고
    • A proof of a conjecture of David Kendall on the shape of random polygons of large area
    • (in Russian) English translation: Cybernet. Systems Anal., 33, 461-467
    • Kovalenko, I. N. (1997). A proof of a conjecture of David Kendall on the shape of random polygons of large area. Kibernet. Sistem. Anal. 1997, 3-10, 187 (in Russian). English translation: Cybernet. Systems Anal. 33, 461-467.
    • (1997) Kibernet. Sistem. Anal. , vol.1997 , Issue.187 , pp. 3-10
    • Kovalenko, I.N.1
  • 9
    • 2942518837 scopus 로고    scopus 로고
    • An extension of a conjecture of D. G. Kendall concerning shapes of random polygons to Poisson Voronoï cells
    • (in Ukranian). English translation: in Voronoï's Impact on Modern Science, eds P. Engel et al., Institute of Mathematics, Kyiv, pp. 266-274
    • Kovalenko, I. N. (1998). An extension of a conjecture of D. G. Kendall concerning shapes of random polygons to Poisson Voronoï cells. Proc. Inst. Math. Nat. Acad. Sci. Ukr. Math. Appl. 212, 266-274 (in Ukranian). English translation: in Voronoï's Impact on Modern Science, eds P. Engel et al., Institute of Mathematics, Kyiv, pp. 266-274.
    • (1998) Proc. Inst. Math. Nat. Acad. Sci. Ukr. Math. Appl. , vol.212 , pp. 266-274
    • Kovalenko, I.N.1
  • 10
    • 0012483780 scopus 로고    scopus 로고
    • A simplified proof of a conjecture of D. G. Kendall concerning shapes of random polygons
    • Kovalenko, I. N. (1999). A simplified proof of a conjecture of D. G. Kendall concerning shapes of random polygons. J. Appl. Math. Stoch. Anal. 12, 301-310.
    • (1999) J. Appl. Math. Stoch. Anal. , vol.12 , pp. 301-310
    • Kovalenko, I.N.1
  • 11
    • 0000819875 scopus 로고
    • A heuristic proof of a long-standing conjecture of D. G. Kendall concerning the shapes of certain large random polygons
    • Miles, R. E. (1995). A heuristic proof of a long-standing conjecture of D. G. Kendall concerning the shapes of certain large random polygons. Adv. Appl. Prob. 27, 397-417.
    • (1995) Adv. Appl. Prob. , vol.27 , pp. 397-417
    • Miles, R.E.1
  • 13
    • 7444266554 scopus 로고    scopus 로고
    • A review on probabilistic models and results for Voronoi tessellations
    • (in Ukranian). English translation: in Voronoï's Impact on Modern Science, eds P. Engel et al., Institute of Mathematics, Kyiv, 254-265
    • Møller, J. (1998). A review on probabilistic models and results for Voronoi tessellations. Proc. Inst. Math. Nat. Acad. Sci. Ukr. Math. Appl. 212, 254-265 (in Ukranian). English translation: in Voronoï's Impact on Modern Science, eds P. Engel et al., Institute of Mathematics, Kyiv, pp. 254-265.
    • (1998) Proc. Inst. Math. Nat. Acad. Sci. Ukr. Math. Appl. , vol.212 , pp. 254-265
    • Møller, J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.