Séminaire Lotharingien de Combinatoire, B70b (2014), 27 pp.

Cédric Lecouvey, Emmanuel Lesigne and Marc Peigné

Conditioned One-Way Simple Random Walk and Combinatorial Representation Theory

Abstract. A one-way simple random walk is a random walk in the quadrant Z+n whose increments are elements of the canonical base. In relation with representation theory of Lie algebras and superalgebras, we describe the law of such a random walk conditioned to stay in a closed octant, a semi-open octant, or other types of semi-groups. The combinatorial representation theory of these algebras allows us to describe a generalized Pitman transformation which realizes the conditioning on the set of paths of the walk. We pursue here a direction initiated by O'Connell and his coauthors, and also developed by the authors.

Received: April 11, 2013. Accepted: September 16, 2013.

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