Abstract
Let (Xi : i ≥ 1) be i.i.d. points in ℝd, d ≥ 2, and let Tn be a minimal spanning tree on (X1, Xn). Let L((X1, Xn)) be the length of Tn and for each strictly positive integer α let N((X1, . . ., Xn); α) be the number of vertices of degree α in Tn. If the common distribution satisfies certain regularity conditions, then we prove central limit theorems for L((X1, . . ., Xn)) and N((X1, . . ., Xn); α). We also study the rate of convergence for EL((X1, . . ., Xn)).
Original language | English |
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Pages (from-to) | 969-984 |
Number of pages | 16 |
Journal | Advances in Applied Probability |
Volume | 31 |
Issue number | 4 |
DOIs | |
Publication status | Published - 1999 |
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Applied Mathematics