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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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