A proof of the Markov chain tree theorem

Anantharam, Venkat; Tsoucas, Pantelis

doi:10.1016/0167-7152(89)90016-3

Cited by 62 publications

(95 citation statements)

References 4 publications

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“…We conclude this section by observing that the Markov chain tree theorem (see, for example, [1]) allows to compute the root distribution when conditioning on P( q ), the partition of X that is associated with q . We write…”

Section: And For Anymentioning

confidence: 99%

Two Applications of Random Spanning Forests

Avena

Gaudillière

2017

J Theor Probab

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We use random spanning forests to find, for any Markov process on a finite set of size n and any positive integer 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.

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Section: And For Anymentioning

confidence: 99%

Two Applications of Random Spanning Forests

Avena

Gaudillière

2017

J Theor Probab

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“…Alternatively, one can put a probability distribution on the edges emanating from each vertex, and stipulate that the new edge is to be chosen at random. This gives the tree-walk introduced by Anantharam and Tsoucas [AT89] in their proof of the Markov chain tree theorem of Leighton and Rivest [LR86].…”

Section: Lemma 319 [Ll07]mentioning

confidence: 99%

Chip-Firing and Rotor-Routing on Directed Graphs

Holroyd

Levine

Mészáros

et al. 2008

Progress in Probability

140

298

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“…This core result has appeared in a variety of different contexts [1,2,6,14,23,24]. It was discovered by Shubert [22] in connection with flow-graph methods, and independently by Kohler and Vollmerhaus [15] motivated by problems in biological modelling.…”

Section: Then Amentioning

confidence: 95%