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 |
|---|---|
| Pages (from-to) | 969-984 |
| Number of pages | 16 |
| Journal | Advances in Applied Probability |
| Volume | 31 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - 1999 Jan 1 |
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All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Applied Mathematics
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The central limit theorem for euclidean minimal spanning trees II. / Lee, Sung chul.
In: Advances in Applied Probability, Vol. 31, No. 4, 01.01.1999, p. 969-984.Research output: Contribution to journal › Article
TY - JOUR
T1 - The central limit theorem for euclidean minimal spanning trees II
AU - Lee, Sung chul
PY - 1999/1/1
Y1 - 1999/1/1
N2 - 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)).
AB - 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)).
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UR - http://www.scopus.com/inward/citedby.url?scp=0033315088&partnerID=8YFLogxK
U2 - 10.1239/aap/1029955253
DO - 10.1239/aap/1029955253
M3 - Article
VL - 31
SP - 969
EP - 984
JO - Advances in Applied Probability
JF - Advances in Applied Probability
SN - 0001-8678
IS - 4
ER -