Journal of Theoretical Probability

, Volume 2, Issue 1, pp 129–146 | Cite as

Some sample path properties of a random walk on the cube

  • Peter Matthews


Some properties of the set of vertices not visited by a random walk on the cube are considered. The asymptotic distribution of the first timeQ this set is empty is derived. The distribution of the number of vertices not visited is found for times nearEQ. Next the first time all unvisited vertices are at least some distanced apart is explored. Finally the expected time taken by the path to come within a distanced of all points is calculated. These results are compared to similar results for random allocations.

Key Words

Random allocation cube random walk covering problems 


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Copyright information

© Plenum Publishing Corporation 1989

Authors and Affiliations

  • Peter Matthews
    • 1
  1. 1.Department of Mathematics and StatisticsUniversity of Maryland Baltimore CountyBaltimore

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