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].
Cite
@article{arxiv.1202.3604,
title = {Conditioned one-way simple random walk and representation theory},
author = {Cédric Lecouvey and Emmanuel Lesigne and Marc Peigné},
journal= {arXiv preprint arXiv:1202.3604},
year = {2012}
}
Comments
32 pages