On the Expected Distance of a Random Walk
May 2015 | Hale, Trevor
This paper investigates the Euclidean length of a random walk though n co-planar points. The length of which has multiple applications including spanning trees, Steiner trees, and certain forms of the traveling salesman problem. To estimate this distance, we partition an area A into m equivalent squares and then add the expected Euclidean distances traveled between each of the m squares with the expected Euclidean distances traveled within each of the m squares. The end result is a closed form model for the expected length of a random walk through n co-planar points. Some avenues of future research are also included.
- Faizul Huq
- Heather S. Lutz
- Carlos Moslares
International Journal of Mathematics in Operational Research