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On the expected distance of a random walk

Author

Listed:
  • Trevor S. Hale
  • Faizul Huq
  • Heather Lutz
  • Carles Moslares

Abstract

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.

Suggested Citation

  • Trevor S. Hale & Faizul Huq & Heather Lutz & Carles Moslares, 2015. "On the expected distance of a random walk," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 7(3), pages 241-250.
    • Handle: RePEc:ids:ijmore:v:7:y:2015:i:3:p:241-250
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    Cited by:

    1. Martin Wiegand & Saralees Nadarajah, 2024. "On the expected length of an orderly path," OPSEARCH, Springer;Operational Research Society of India, vol. 61(2), pages 963-971, June.
    2. Heather S. Lutz & Trevor S. Hale & Faizul Huq, 2020. "Technical note: the expected length of an orderly path," Annals of Operations Research, Springer, vol. 289(2), pages 463-472, June.

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