Random walk in an alcove of an affine Weyl group, and non-colliding random walks on an interval

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:97

Article

关键词: random walk;    affine Weyl group;    lattice path enumeration;    reflection principle;    Weyl chamber;    alcove;   

DOI  :  10.1006/jcta.2001.3216

来源: Elsevier

【 摘 要 】

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 > x(1) > x(2) > (. . .) > x(n) > 0, which is a resealed alcove of the affine Weyl group (C) over tilde (n). If each coordinate is considered to be an independent particle, this models n non-colliding random walks on the interval (0, m). Another case models n non-colliding random walks on a circle. (C) 2001 Elsevier Science.

【 授权许可】

Free