A proof of the Vershik-Prohorov conjecture on the universality of the limit shape for a class of random polygonal lines

L. 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 Back