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Conditioned Random Walk in Weyl Chambers and Renewal Theory
[chapter]
2013
Springer Proceedings in Mathematics & Statistics
We present here the main result from [7] and explain how to use Kashiwara crystal basis theory to associate a random walk to each minuscule irreducible representation V of a simple Lie algebra; the generalized Pitman transform defined in [1] for similar random walks with uniform distributions yields yet a Markov chain when the crystal attached to V is endowed with a probability distribution compatible with its weight graduation. The main probabilistic argument in our proof is a quotient version
doi:10.1007/978-3-642-38806-4_11
fatcat:oiv46prgwrcdfbrajczshkvcjy