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Conditioned one-way simple random walk and representation theory

Abstract : We call one-way simple random walk a random walk in the quadrant Z₊ⁿ whose increments belong to 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 in a direction initiated by O'Connell and his coauthors [13,14,2], and also developed in [12]. Our work relies on crystal bases theory and insertion schemes on tableaux described by Kashiwara and his coauthors in [1] and, very recently, in [5].
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Contributor : Cédric Lecouvey Connect in order to contact the contributor
Submitted on : Thursday, February 16, 2012 - 11:13:55 AM
Last modification on : Tuesday, January 11, 2022 - 5:56:08 PM
Long-term archiving on: : Thursday, May 17, 2012 - 2:26:55 AM


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  • HAL Id : hal-00670834, version 1
  • ARXIV : 1202.3604



Cédric Lecouvey, Emmanuel Lesigne, Marc Peigné. Conditioned one-way simple random walk and representation theory. SLC, 2013. ⟨hal-00670834⟩



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