On the expected distance of a random walk
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Copyright © 2015 Inderscience Enterprises Ltd. 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.
author list (cited authors)
Hale, T. S., Huq, F., Lutz, H., & Moslares, C.