Random walks in Weyl chambers and crystals

@inproceedings{Lecouvey2012RandomWI,
  title={Random walks in Weyl chambers and crystals},
  author={C'edric Lecouvey and Emmanuel Lesigne and Marc Peign'e},
  year={2012}
}
We use Kashiwara crystal basis theory to associate a random walk W to each irreducible representation V of a simple Lie algebra. This is achieved by endowing the crystal attached to V with a (possibly non-uniform) probability distribution compatible with its weight graduation. We then prove that the generalized Pitman transform defined for similar random walks with uniform distributions yields yet another Markov chain. When the representation is minuscule, and the associated random walk has a… CONTINUE READING
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