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Two Applications of Random Spanning Forests

Author

Listed:
  • L. Avena

    (University of Leiden)

  • A. Gaudillière

    (Aix Marseille University)

Abstract

We use random spanning forests to find, for any Markov process on a finite set of size n and any positive integer $$m \le n$$ m ≤ n , a probability law on the subsets of size m such that the mean hitting time of a random target that is drawn from this law does not depend on the starting point of the process. We use the same random forests to give probabilistic insights into the proof of an algebraic result due to Micchelli and Willoughby and used by Fill and by Miclo to study absorption times and convergence to equilibrium of reversible Markov chains. We also introduce a related coalescence and fragmentation process that leads to a number of open questions.

Suggested Citation

  • L. Avena & A. Gaudillière, 2018. "Two Applications of Random Spanning Forests," Journal of Theoretical Probability, Springer, vol. 31(4), pages 1975-2004, December.
    • Handle: RePEc:spr:jotpro:v:31:y:2018:i:4:d:10.1007_s10959-017-0771-3
    DOI: 10.1007/s10959-017-0771-3
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    References listed on IDEAS

    as
    1. James Allen Fill, 2009. "On Hitting Times and Fastest Strong Stationary Times for Skip-Free and More General Chains," Journal of Theoretical Probability, Springer, vol. 22(3), pages 587-600, September.
    2. Anantharam, V. & Tsoucas, P., 1989. "A proof of the Markov chain tree theorem," Statistics & Probability Letters, Elsevier, vol. 8(2), pages 189-192, June.
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