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On mean recurrence times of Markov chains and spanning tree invariants

✍ Scribed by Ricardo Gómez

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
141 KB
Volume
433
Category
Article
ISSN
0024-3795

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✦ Synopsis

We show that the mean recurrence times of (countable state) irreducible and positively recurrent Markov chains are the spanning tree invariants of the first return loop systems. Then, by the Perron-Frobenius Theorem, the spanning tree invariants of the first return loop systems of a finite state Markov chain are all equal if and only if the process is doubly stochastic, settling a conjecture on a question in G ómez and Salazar-Montiel (2010) [1] where it was verified for matrices of size at most three.

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