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Random Walk in the Complete Graph : Hitting and Cover Times

Author

Listed:
  • François Castella

    (University of Rennes)

  • Bruno Sericola

    (Inria)

Abstract

We consider the moments and the distribution of the hitting and cover times of a random walk in the complete graph. We study both the time needed to reach any subset of states and the time needed to visit all the states of a subset at least once. We obtain recurrence relations for the moments of all orders and we use these relations to analyze the asymptotic behavior of the hitting and cover times distributions when the number of states tends to infinity.

Suggested Citation

  • François Castella & Bruno Sericola, 2025. "Random Walk in the Complete Graph : Hitting and Cover Times," Methodology and Computing in Applied Probability, Springer, vol. 27(2), pages 1-23, June.
    • Handle: RePEc:spr:metcap:v:27:y:2025:i:2:d:10.1007_s11009-025-10166-6
    DOI: 10.1007/s11009-025-10166-6
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