Markov chains in a Dirichlet environment and hypergeometric integrals

Abstract: The aim of this Note is to establish some relations between Markov chains in Dirichlet Environments on directed graphs and certain hypergeometric integrals associated with a particular arrangement of hyperplanes. We deduce some new relations on important functionals of the Markov chain. From these relations and the computation of the connexion obtained by moving one hyperplane of the arrangement. To cite this article: C. Sabot, C. R. Acad. Sci. Paris, Ser. I 342 (2006). [Copyright &y& Elsevier]