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

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