On the expected distance of a random walk. (2015)

• Record Type: Journal Article
• Authors: Hale, Trevor S.; Huq, Faizul; Lutz, Heather; Moslares, Carles
• Is Part Of: International journal of mathematics in operational research. Volume 7:Number 3(2015)
• Page Start: 241
• Page End: 250
• Publication Date: 2015
• Subjects: expected distance -- random walk -- Euclidean TSP -- travelling salesman problem -- Euclidean distances -- Euclidean length; Operations research -- Mathematical models -- Periodicals; Operations research -- Mathematics -- Periodicals; Decision making -- Mathematical models -- Periodicals; 658.4033
• Languages: English
• ISSNs: 1757-5850

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.