메뉴 건너뛰기




Volumn 41, Issue 1, 2009, Pages 38-62

Nearest-neighbor graphs on the Cantor set

Author keywords

Cantor set; Law of large numbers; Nearest neighbor

Indexed keywords

ASYMPTOTICS; CANTOR SET; CANTOR SETS; EDGE LENGTH; LAW OF LARGE NUMBERS; NEAREST NEIGHBOR; RANDOM GRAPHS; RESCALING;

EID: 67649669747     PISSN: 00018678     EISSN: None     Source Type: Journal    
DOI: 10.1239/aap/1240319576     Document Type: Article
Times cited : (1)

References (15)
  • 2
    • 14544281094 scopus 로고    scopus 로고
    • Gaussian limits for random measures in geometric probability
    • BARYSHNIKOV, Y. AND YUKICH, J.E. (2005). Gaussian limits for random measures in geometric probability. Ann. Appl. Prob. 15, 213-253.
    • (2005) Ann. Appl. Prob , vol.15 , pp. 213-253
    • BARYSHNIKOV, Y.1    YUKICH, J.E.2
  • 3
    • 67649655705 scopus 로고    scopus 로고
    • BROMWICH, T.J. (1942). An Introduction to the Theory of Infinite Series. Macmillan and Company.
    • BROMWICH, T.J. (1942). An Introduction to the Theory of Infinite Series. Macmillan and Company.
  • 4
    • 21444442608 scopus 로고    scopus 로고
    • The standard Cantor function is subadditive
    • DOBOS, J. (1996). The standard Cantor function is subadditive. Proc. Amer. Math. Soc. 124, 3425-3426.
    • (1996) Proc. Amer. Math. Soc , vol.124 , pp. 3425-3426
    • DOBOS, J.1
  • 6
    • 0345890592 scopus 로고
    • General spacefilling curve heuristics and limit theory for the traveling salesman problem
    • GAO, J. AND STEELE, J. M. (1994). General spacefilling curve heuristics and limit theory for the traveling salesman problem. J. Complexity 10, 230-245.
    • (1994) J. Complexity , vol.10 , pp. 230-245
    • GAO, J.1    STEELE, J.M.2
  • 7
    • 0031592716 scopus 로고    scopus 로고
    • Function a literations and periodic oscillations for simple random walk on the Sierpińskigraph
    • GRABNER, P.J. AND WOESS, W. (1997). Function a literations and periodic oscillations for simple random walk on the Sierpińskigraph. Stoch. Process. Appl. 69, 127-138.
    • (1997) Stoch. Process. Appl , vol.69 , pp. 127-138
    • GRABNER, P.J.1    WOESS, W.2
  • 8
    • 16144366396 scopus 로고    scopus 로고
    • Explicit and asymptotic formulae for the expected values of the order statistics of the Cantor distribution
    • KNOPFMACHER, A. AND PRODINGER, H. (1996). Explicit and asymptotic formulae for the expected values of the order statistics of the Cantor distribution. Statist. Prob. Lett. 27, 189-194.
    • (1996) Statist. Prob. Lett , vol.27 , pp. 189-194
    • KNOPFMACHER, A.1    PRODINGER, H.2
  • 9
    • 84974324435 scopus 로고
    • Traveling salesman with a self-similar itinerary
    • LALLEY, S. (1990). Traveling salesman with a self-similar itinerary. Prob. Eng. Inf. Sci. 4, 1-18.
    • (1990) Prob. Eng. Inf. Sci , vol.4 , pp. 1-18
    • LALLEY, S.1
  • 10
    • 0041707236 scopus 로고    scopus 로고
    • Central limit theorems for κ-nearest neighbour distances
    • PENROSE, M. (2000).Central limit theorems for κ-nearest neighbour distances. Stoch. Process. Appl. 85, 295-320.
    • (2000) Stoch. Process. Appl , vol.85 , pp. 295-320
    • PENROSE, M.1
  • 11
    • 0036117358 scopus 로고    scopus 로고
    • Limit theory for random sequential packing and deposition
    • PENROSE, M.D. AND YUKICH, J.E. (2002). Limit theory for random sequential packing and deposition. Ann. Appl. Prob. 12, 272-301.
    • (2002) Ann. Appl. Prob , vol.12 , pp. 272-301
    • PENROSE, M.D.1    YUKICH, J.E.2
  • 12
    • 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
  • 13
    • 0024750851 scopus 로고
    • Spacefilling curves and the planar traveling salesman problem
    • Mach
    • PLATZMAN, L. K. AND BARTHOLDI, J. J., III. (1989). Spacefilling curves and the planar traveling salesman problem. J. Assoc. Comput. Mach. 36, 719-737.
    • (1989) J. Assoc. Comput , vol.36 , pp. 719-737
    • PLATZMAN, L.K.1    BARTHOLDI III, J.J.2
  • 14
    • 67649644311 scopus 로고    scopus 로고
    • STEELE, J.M. (1997). Probability Theory and Combinatorial Optimization. Society for Industrial and Applied Mathematics, Philadelphia, PA.
    • STEELE, J.M. (1997). Probability Theory and Combinatorial Optimization. Society for Industrial and Applied Mathematics, Philadelphia, PA.
  • 15
    • 67649653711 scopus 로고    scopus 로고
    • YUKICH, J.E. (1998). Probability Theory of Classical Euclidean Optimization Problems (Lecture Notes Math. 1675). Springer, Berlin.
    • YUKICH, J.E. (1998). Probability Theory of Classical Euclidean Optimization Problems (Lecture Notes Math. 1675). Springer, Berlin.


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.