Geodesic
Conditioned One-Way Simple Random Walk and Combinatorial Representation Theory
Séminaire lotharingien de combinatoire, Tome 70 (2013-2014)

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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. 

@article{SLC_2013-2014_70_a1,
     author = {C\'edric Lecouvey and Emmanuel Lesigne and Marc Peign\'e},
     title = {Conditioned {One-Way} {Simple} {Random} {Walk} and {Combinatorial} {Representation} {Theory}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {70},
     year = {2013-2014},
     url = {http://geodesic.mathdoc.fr/item/SLC_2013-2014_70_a1/}
}
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AU  - Cédric Lecouvey
AU  - Emmanuel Lesigne
AU  - Marc Peigné
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Cédric Lecouvey; Emmanuel Lesigne; Marc Peigné. Conditioned One-Way Simple Random Walk and Combinatorial Representation Theory. Séminaire lotharingien de combinatoire, Tome 70 (2013-2014). http://geodesic.mathdoc.fr/item/SLC_2013-2014_70_a1/