Polynomials Associated with Finite Markov Chains

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.

References

  1. 1.
    V. Anantharam, P. Tsoucas, A proof of the Markov chain tree theorem. Stat. Probab. Lett. 8(2), 189–192 (1989)MATHMathSciNetCrossRefGoogle Scholar
  2. 2.
    R. Lyons, Y. Peres, Probability on trees and networks (2014), http://pages.iu.edu/~rdlyons/prbtree/prbtree.html

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.CNRS, Laboratoire d’Informatique Institut Gaspard MongeUniversité Paris-Est 5 bd DescartesMarne-la-Vallée Cedex 2France

Personalised recommendations