Random Triangles in a Metric Space of Sequences

Abstract

We investigate probabilistic properties of random triangles in the space of finite sequences with the Hamming metrics. As a triangle is understood any triple of points with distances between them. Probability measure is given by the classical way. In particular, it is shown that randomly chosen triangle is approximately equilateral with high probability. We also introduce a quantity that characterizes degree of “equilaterality” of triangles in the metric space in average.