no. 1
Probability Theory/Differential Geometry
Markov chains in a Dirichlet environment and hypergeometric integrals
[Chaînes de Markov en environnement de Dirichlet et intégrales hypergéométriques]

Présenté par : Paul Malliavin

Sabot, Christophe1
1 CNRS, UMPA, ENS Lyon, 46 allée d'Italie, 69007 Lyon, France
Comptes Rendus. Mathématique, Tome 342 (2006) no. 1, pp. 57-62.

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.

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.

Reçu le :
Accepté le :
Publié le :
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, Tome 342 (2006) no. 1, pp. 57-62. doi : 10.1016/j.crma.2005.10.028. http://archive.numdam.org/articles/10.1016/j.crma.2005.10.028/

[1] Enriquez, N.; Sabot, C. Edge oriented reinforced random walks and RWRE, C. R. Math. Acad. Sci. Paris, Ser. I, Volume 335 (2002) no. 11, pp. 941-946

[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

[4] Propp, J.G.; Wilson, D.B. How to get a perfectly random sample from a generic Markov chain and generate a random spanning tree of a directed graph, J. Algorithms, Volume 27 (1998), pp. 170-217

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