Probability Theory/Differential Geometry
Markov chains in a Dirichlet environment and hypergeometric integrals
Comptes Rendus. Mathématique, Volume 342 (2006) no. 1, pp. 57-62.

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.

Le but de cette Note est d'établir une relation entre les chaînes de Markov en environnement de Dirichlet sur des graphes orientés, et certaines intégrales hypergéométriques associées à un arrangement d'hyperplans. Nous déduisons du calcul de la connexion obtenue en bougeant un hyperplan des relations nouvelles sur des fonctionnelles importantes de ces marches.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2005.10.028
Sabot, Christophe 1

1 CNRS, UMPA, ENS Lyon, 46 allée d'Italie, 69007 Lyon, France
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Sabot, Christophe. Markov chains in a Dirichlet environment and hypergeometric integrals. Comptes Rendus. Mathématique, Volume 342 (2006) no. 1, pp. 57-62. doi : 10.1016/j.crma.2005.10.028. http://www.numdam.org/articles/10.1016/j.crma.2005.10.028/

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[2] Enriquez, N.; Sabot, C. Random walks in a Dirichlet environment http://hal.ccsd.cnrs.fr/ccsd-00011153

[3] Orlik, P.; Terao, H. Arrangements and Hypergeometric Integrals, MSJ Memoirs, vol. 9, Math. Soc. Japan, Tokyo, 2001

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