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N. Dolbilin and M. Tanemura studied the convex hulls of finite subsets of theClifford torus $T$ in $E^4$. They have completely studied the combinatorialstructure of the convex hull for a periodic point set. Moreover, there wasperformed a numerical simulation of the convex hull for the Poisson pointprocess on $T$ that showed that the mean valence of a vertex of the convex hullhas asymptotics $O^*(\ln \lambda)$ where $\lambda$ is the rate of the process.  N. Dolbilin suggested the author to prove the conjecture on the logarithmicgrowth of the mean degree of a vertex.  In this paper we prove this conjecture and some related theorems.

Asymptotics for some combinatorial characteristics of the convex hull of a Poisson point process in the Clifford torus