Two Applications of Random Spanning Forests

L. Avena () and A. Gaudillière ()
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L. Avena: University of Leiden
A. Gaudillière: Aix Marseille University

Journal of Theoretical Probability, 2018, vol. 31, issue 4, 1975-2004

Abstract: 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.

Keywords: Finite networks; Spectral analysis; Spanning forests; Determinantal processes; Random sets; Hitting times; Coalescence and fragmentation; Local equilibria; Primary: 05C81; 60J20; 15A15; Secondary: 15A18; 05C85 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10959-017-0771-3

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