Aleksandr Mysliuk

Asymptotic probability of a fixed edge being on the boundary of the convex hull of a random walk in $\mathbb{Z}^2$

A simple symmetric random walk in the space $\mathbb{Z}^2$ is considered. The asymptotic behavior as the number of jumps tends to infinity of the probability that a fixed edge of the random walk lies in the polygon that forms the boundary of the convex hull is investigated.