Random Walk in an Alcove of an Affine Weyl Group, and Non-colliding Random Walks on an Interval

@article{Grabiner2002RandomWI,
  title={Random Walk in an Alcove of an Affine Weyl Group, and Non-colliding Random Walks on an Interval},
  author={David J. Grabiner},
  journal={J. Comb. Theory, Ser. A},
  year={2002},
  volume={97},
  pages={285-306}
}
Abstract. We use a reflection argument, introduced by Gessel and Zeilberger, to count the number of k-step walks between two points which stay within a chamber of a Weyl group. We apply this technique to walks in the alcoves of the classical affine Weyl groups. In all cases, we get determinant formulas for the number of k-step walks. One important example is the region m > x1 > x2 > · · · > xn > 0, which is a rescaled alcove of the affine Weyl group C̃n. If each coordinate is considered to be… CONTINUE READING
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