Abstract
We present a proof of the theorem which states that a matrix of Euclidean distances on a set of specially distributed random points in the n-dimensional Euclidean space R n converges in probability to an ultrametric matrix as n → ∞. Values of the elements of an ultrametric distance matrix are completely determined by variances of coordinates of random points. Also we present a probabilistic algorithm for generation of finite ultrametric structures of any topology in high-dimensional Euclidean space. Validity of the algorithm is demonstrated by explicit calculations of distance matrices and ultrametricity indexes for various dimensions n.
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Zubarev, A.P. On stochastic generation of ultrametrics in high-dimensional Euclidean spaces. P-Adic Num Ultrametr Anal Appl 6, 155–165 (2014). https://doi.org/10.1134/S2070046614020046
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DOI: https://doi.org/10.1134/S2070046614020046