### Abstract

Let {X_{i}: i ≥ 1} be i.i.d. with uniform distribution [- 1/2, 1/2]^{d}, d ≥ 2, and let T_{n} be a minimal spanning tree on {X_{1},..., X_{n}}. For each strictly positive integer α, let N({X_{1},..., X_{n}}; α) be the number of vertices of degree α in T_{n}. Then, for each α such that P(N({X_{1},..., X_{α+1}}; α) = 1) > 0, we prove a central limit theorem for N({X_{1},..., X_{n}}; α).

Original language | English |
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Pages (from-to) | 996-1020 |

Number of pages | 25 |

Journal | Annals of Applied Probability |

Volume | 7 |

Issue number | 4 |

Publication status | Published - 1997 Nov |

### All Science Journal Classification (ASJC) codes

- Statistics and Probability
- Statistics, Probability and Uncertainty

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## Cite this

Lee, S. (1997). The central limit theorem for Euclidean minimal spanning trees I.

*Annals of Applied Probability*,*7*(4), 996-1020.