Markov chains in a Dirichlet Environment and hypergeometric integrals

Christophe Sabot (1)

1 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées

The aim of this text 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 from these relations and the computation of the connexion obtained by moving one hyperplane of the arrangement some new relations on important functionals of the Markov chain.

Mots clés: Markov chains; Random environments; hypergeometric integrals; arrangement of hyperplanes.; arrangement of hyperplanes

Domaines: Probabilités [math.PR]; Géométrie différentielle [math.DG]

Christophe Sabot. Markov chains in a Dirichlet Environment and hypergeometric integrals. Comptes rendus de l'Académie des sciences. Série I, Mathématique, 2002, 335 (11), pp.941-946. ⟨10.1016/S1631-073X(02)02580-3⟩. ⟨hal-00011151⟩