Asymptotics for Voronoi tessellations on random samples

Stochastic Processes and their Applications

Volumn 83, Issue 2, 1999, Pages 273-288

  McGivney, K ^a   Yukich, J E ^b  

^a University of Arizona   (United States)

^b LEHIGH UNIVERSITY   (United States)

Author keywords

Complete convergence; Delaunay triangulation; Subadditive and superadditive Euclidean functionals; Voronoi tessellation

Indexed keywords

EID: 0033210542     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-4149(99)00035-6     Document Type: Article

References (20)

1. Aurenhammer, F., 1991. Voronoi diagrams - A survey of a fundamental geometric data structure. ACM Comput. Surv. 23 (3), 345-405.
2. Avram, F., Bertsimas, D., 1993. On central limit theorems in geometrical probability. Ann. Appl. Probab. 3 (4), 1033-1046.
3. Azuma, K., 1967. Weighted sums of certain dependent random variables. Tohuku Math. J. 19, 357-367.
4. Beardwood, J., Halton, J.H., Hammersley, J.M., 1959. The shortest path through many points. Proc. Cambridge Philos. Soc. 55, 299-327.
5. Chalker, T.K., Godbole, A.P., Hitczenko, P., Radcliff, J., Ruehr, O.G., 1999. On the size of a random sphere of influence graph. Adv. Appl. Probab., in press.
6. Christ, N.H., Friedberg, R., Lee, T.D., 1982. Random lattice field theory: General formulation. Nucl. Phys. B 202, 89-125.
7. Drouffe, J.M., Itzykson, C., 1984. Random geometry and statistics of two dimensional cells. Nucl. Phys. B 235, 45-53.
8. Jerauld, G.R., Hatfield, J.C., Scriven, L.E., Davis, H.T., 1984. Percolation and conduction on Voronoi and triangular networks: A case study in topological disorder. J. Phys. C 17, 1519-1529.
9. McGivney, K., 1997. Probabilistic Limit Theorems for Combinatorial Optimization Problems. Ph.D. Thesis, Lehigh University.
10. Miles, R.E., 1970. On the homogeneous planar point process. Math. Biosci. 6, 85-127.
11. Moller, J., 1994. Lectures on random Voronoi tessellations. Lecture Notes in Statistics, Vol. 87. Springer, Berlin.
12. Okabe, A., Boots, B., Sugihara, K., 1992. Spatial Tessellations - Concepts and Applications of Voronoi Diagrams. Wiley, England.
13. Preparata, F.P., Shamos, M.I., 1985. Computational Geometry, An Introduction. Springer, Berlin.
14. Redmond, C., Yukich, J.E., 1994. Limit theorems and rates of convergence for subadditive Euclidean functionals. Ann. Appl. Probab. 4 (4), 1057-1073.
15. Redmond, C., Yukich, J.E., 1996. Asymptotics for Euclidean functionals with power weighted edges. Stochast. Process. Appl. 61, 289-304.
16. Steele, J.M., 1997. Probability theory and combinatorial optimization, Vol. 69. CBMS-NSF Regional Conference Series in Applied Mathematics, SIAM, Philadelphia.
17. Stoyan, D., Kendall, W.S., Mecke, J., 1995. Stochastic Geometry and Its Applications, 2nd Edition. Wiley, New York.
18. Talagrand, M., 1995. Concentration of measure and isoperimetric inequalities in product spaces. I.H.E.S. 81, 73-205.
19. Weide, B., 1978. Statistical Methods in Algorithm Design and Analysis. Ph.D. Thesis, Computer Science Department, Carnegie Mellon University.
20. Yukich, J.E., 1998. Probability theory of classical Euclidean optimization problems. Lecture Notes in Mathematics, Vol. 1675. Springer, Berlin.