On a random directed spanning tree

Advances in Applied Probability

Volumn 36, Issue 1, 2004, Pages 19-42

  Bhatt, Abhay G ^a   Roy, Rahul ^a  

^a INDIAN STATISTICAL INSTITUTE   (India)

Author keywords

Minimal spanning tree; Record values; Weak convergence

Indexed keywords

MINIMAL SPANNING TREE; RECORD VALUES; WEAK CONVERGENCE;

ASYMPTOTIC STABILITY; CONVERGENCE OF NUMERICAL METHODS; POISSON DISTRIBUTION; SET THEORY; STATISTICAL METHODS; THEOREM PROVING;

TREES (MATHEMATICS);

EID: 1842457648     PISSN: 00018678     EISSN: None     Source Type: Journal    
DOI: 10.1239/aap/1077134462     Document Type: Article

References (13)

1. ALDOUS, D. AND STEELE, J. M. (1992). Asymptotics for Euclidean minimal spanning trees on random points. Prob. Theory Relat. Fields 92, 247-258.
2. BEARDWOOD, J., HALTON, J. H. AND HAMMERSLEY, J. M. (1959). The shortest path through many points. Proc. Camb. Phil. Soc. 55, 299-327.
3. CHUNG, K. L. (1974). A Course in Probability Theory, 2nd edn. Academic Press, New York.
4. DAVID H. A. (1970). Order Statistics. John Wiley, New York.
5. FELLER, W. (1978). An Introduction to Probability Theory and Its Applications, Vol. 1. John Wiley, New York.
6. GILBERT, E. N. (1961). Random plane networks. J. Soc. Indust. Appl. 9, 533-543.
7. GRADSHTEYN, I. S. AND RYZHIK, I. M. (1980). Table of Integrals, Series and Products. Academic Press, New York.
8. GUPTA, P AND KUMAR, P. R. (1999). Critical power for asymptotic connectivity in wireless networks. In Stochastic Analysis, Control, Optimization and Applications, eds W. M. McEneaney, G. Yin and Q. Zhang, Birkhäuser, Boston, MA, pp. 547-566.
9. KESTEN, H. AND LEE, S. (1996). The central limit theorem for weighted minimal spanning trees on random points. Ann. Appl. Prob. 6, 495-527.
10. RÉNYI, A. (1976). On the extreme elements of observations. In Selected Papers of Alfred Rényi, Vol. 3, Akadémiai Kiadó, Budapest, pp. 50-65.
11. RODRIGUEZ-ITURBE, I. AND RINALDO, A. (1997). Fractal River Basins, Chance and Self-Organization. Cambridge University Press, New York.
12. SHOHAT, J. A. AND TAMARKIN, J. D. (1950). The Problem of Moments, revised edn (Math. Surveys 1). American Mathematical Society, New York.
13. STEELE, J. M. (1988). Growth rates of Euclidean minimal spanning trees with power weighted edges. Ann. Prob. 16, 1767-1787.