Abstract
Kesten and Lee [Ann. Appl. Probab. 6 (1996) 495–527] proved that the total length of a minimal spanning tree on certain random point configurations in
The contribution of this paper is twofold. First, we develop a general technique to compute convergence rates in central limit theorems satisfied by minimal spanning trees on sequences of weighted graphs, including minimal spanning trees on Poisson points inside a sequence of growing cubes. Second, we present a way of quantifying the Burton–Keane argument for the uniqueness of the infinite open cluster. The latter is interesting in its own right and based on a generalization of our technique, Duminil-Copin, Ioffe and Velenik [Ann. Probab. 44 (2016) 3335–3356] have recently obtained bounds on probability of two-arm events in a broad class of translation-invariant percolation models.
Citation
Sourav Chatterjee. Sanchayan Sen. "Minimal spanning trees and Stein’s method." Ann. Appl. Probab. 27 (3) 1588 - 1645, June 2017. https://doi.org/10.1214/16-AAP1239
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