Random Walk in an Alcove of an Affine Weyl Group, and Non-Colliding Random Walks on an Interval
| dc.creator | Grabiner, David J. | |
| dc.date | 2000-11-27 | |
| dc.date | 2001-06-04 | |
| dc.date.accessioned | 2026-07-07T04:38:50Z | |
| dc.date.available | 2026-07-07T04:38:50Z | |
| dc.description | 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 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.description | v.2, 22 pages; correction in a definition led to changes in many formulas, also added more background, references, and examples | |
| dc.identifier | https://arxiv.org/abs/math/0011218 | |
| dc.identifier | http://arxiv.org/abs/math/0011218 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/60438 | |
| dc.subject | Combinatorics | |
| dc.subject | Probability | |
| dc.subject | 60G50 (primary), 05A15 (secondary) | |
| dc.title | Random Walk in an Alcove of an Affine Weyl Group, and Non-Colliding Random Walks on an Interval | |
| dc.type | text |