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Recently a general theorem stating that the matrix of normalized Euclidean distances on the set of specially distributed random points in the dimensional Euclidean space   with independent coordinates converges in probability as →∞ to the ultrametric matrix had been proved. The main theorem of the present paper extends this result to the case of weakly correlated coordinates of random points. Prior to formulating and stating this result we give two illustrative examples describing particular algorithms of generation of such nearly ultrametric spaces.

On the Ultrametric Generated by Random Distribution of Points in Euclidean Spaces of Large Dimensions with Correlated Coordinates