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

dc.creatorGrabiner, David J.
dc.date2000-11-27
dc.date2001-06-04
dc.date.accessioned2026-07-07T04:38:50Z
dc.date.available2026-07-07T04:38:50Z
dc.descriptionWe 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 rescaled alcove of the affine Weyl group C_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 the circle.
dc.descriptionv.2, 22 pages; correction in a definition led to changes in many formulas, also added more background, references, and examples
dc.identifierhttps://arxiv.org/abs/math/0011218
dc.identifierhttp://arxiv.org/abs/math/0011218
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/60438
dc.subjectCombinatorics
dc.subjectProbability
dc.subject60G50 (primary), 05A15 (secondary)
dc.titleRandom Walk in an Alcove of an Affine Weyl Group, and Non-Colliding Random Walks on an Interval
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