The central limit theorem for weighted minimal spanning trees on random points

Annals of Applied Probability

Volumn 6, Issue 2, 1996, Pages 495-527

  Kesten, Harry ^a   Lee, Sungchul ^b  

^a Department of Population Medicine and Diagnostic Sciences   (United States)

^b NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

Author keywords

Central limit theorem; Minimal spanning tree

Indexed keywords

EID: 0030501338     PISSN: 10505164     EISSN: None     Source Type: Journal    
DOI: 10.1214/aoap/1034968141     Document Type: Article

References (13)

1. ALDOUS, D. and STEELE, J. M. (1992). Asymptotics for Euclidean minimal spanning trees on random points. Probab. Theory Related Fields 92 247-258.
2. ALEXANDER, K. S. (1994). Rates of convergence of means for distance-minimizing subadditive Euclidean functionals. Ann. Appl. Probab. 4 902-922.
3. ALEXANDER, K. S. (1996). The RSW theorem for continuum percolation and the CLT for Euclidean minimal spanning trees. Ann. Appl. Probab. 6 466-494.
4. AVRAM, F. and BERTSIMAS, D. (1993). On central limit theorems in geometric probability. Ann. Appl. Probab. 3 1033-1046.
5. CHARTRAND, G. and LESNIAK, L. (1986). Graphs and Digraphs. Wadsworth, Belmont, CA.
6. JANSON, S. (1995). The minimal spanning tree in a complete graph and a functional limit theorem for trees in a random graph. Preprint.
7. KRUSKAL, J. B. (1956). On the shortest spanning subtree of a graph and the traveling salesman problem. Proc. Amer. Math. Soc. 7 48-50.
8. LÉVY, P. (1937). Théorie de l'Addition des Variables Aléatoires. Gauthier-Villars, Paris.
9. MCLEISH, D. L. (1974). Dependent central limit theorems and invariance principles. Ann. Probab. 2 620-628.
10. RAMEY, D. B. (1982). A non-parametric test of bimodality with applications to cluster analysis. Ph.D. dissertation, Yale Univ.
11. REDMOND, C. and YUKICH, J. E. (1994). Limit theorems and rates of convergence for Euclidean functionals. Ann. Appl. Probab. 4 1057-1073.
12. STEELE, J. M. (1988). Growth rates of Euclidean minimal spanning trees with power weighted edges. Ann. Probab. 16 1767-1787.
13. TALAGRAND, M. (1995). Concentration of measure and isoperimetric inequalities in product spaces. Publ. Math. vol. 81, Inst. des Mautes Etudes Scientifiques.