Polynomials Associated with Finite Markov Chains

Philippe Biane (1)

1 LIGM - Laboratoire d'Informatique Gaspard-Monge

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.

Domaines: Combinatoire [math.CO]; Probabilités [math.PR]

Philippe Biane. Polynomials Associated with Finite Markov Chains. Séminaire de Probabilités XLVII, Lecture Notes in Mathematics, 2137, Springer, Berlin, 2015., Springer, pp.249-262, 2015. ⟨hal-01098860⟩