Abstract
Given a finite Markov chain, we investigate the first minors of the transition matrix of a lifting of this Markov chain to covering trees. In a simple case we exhibit a nice factorisation of these minors, and we conjecture that it holds more generally.
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References
V. Anantharam, P. Tsoucas, A proof of the Markov chain tree theorem. Stat. Probab. Lett. 8(2), 189–192 (1989)
R. Lyons, Y. Peres, Probability on trees and networks (2014), http://pages.iu.edu/~rdlyons/prbtree/prbtree.html
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Biane, P. (2015). Polynomials Associated with Finite Markov Chains. In: Donati-Martin, C., Lejay, A., Rouault, A. (eds) In Memoriam Marc Yor - Séminaire de Probabilités XLVII. Lecture Notes in Mathematics(), vol 2137. Springer, Cham. https://doi.org/10.1007/978-3-319-18585-9_12
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DOI: https://doi.org/10.1007/978-3-319-18585-9_12
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-18584-2
Online ISBN: 978-3-319-18585-9
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