## A proof of the Vershik-Prohorov conjecture on the universality of the limit shape for a class of random polygonal linesL. V. Bogachev & S. M. Zarbaliev
On the set $\Pi_n$ of all convex polygonal lines on the lattice
$\mathbb{Z}_+^2$, with endpoints $0=(0,0)$ and $n=(n_1,n_2)$ and with
a non-negative slope of all edges, we consider a parametric family of
probability measures $P_n^r$ ($0 |