On the expected distance of a random walk
Summary: This paper investigates the Euclidean length of a random walk though \(n\) coplanar points. The length of which has multiple applications including spanning trees, Steiner trees, and certain forms of the travelling salesman problem. To estimate this distance, we partition an area \(A\) into \(m\) equivalent squares and then add the expected Euclidean distances travelled between each of the \(m\) squares with the expected Euclidean distances travelled within each of the \(m\) squares. The end result is a closed form model for the expected length of a random walk through \(n\) coplanar points. Some avenues of future research are also included.
scientific article; zbMATH DE number 6881384