Appears in collection : Representations, Probability, and Beyond : A Journey into Anatoly Vershik’s World

Let us have two finitely supported probability distributions $\mu, \nu$ on the Euclidean plane, and the cost of transferring of mass $m$ per unit distance is proportional to $m^p$, $0 < p < 1$. Then the optimal transferring of $\mu$ to $\nu$ (the so called Gilbert -- Steiner problem) may have branching points. I want to speak about recent joint result with Danila Cherkashin that the degree of branching points must be equal to 3. The proof relies on the theory of positive definite functions, and so, unites two seemingly far topics, both beloved by Anatoly Moiseevich.