Asymptotics for random walks in alcoves of affine Weyl groups

Details Asymptotics for random walks in alcoves of affine Weyl groups Asymptotics for random walks in alcoves of affine Weyl groups

2003-01-19

arxiv.org/abs/math/0301203v3

S\'eminaire Lotharingien Combin. 52 (2007), Article B52i, 72 pp

Mathematics

Combinatorics

72 pages, AmS-LaTeX; major revision: there are now also theorems on the asymptotic enumeration with non-fixed end points in ty

Scientific paper

Asymptotic results are derived for the number of random walks in alcoves of affine Weyl groups (which are certain regions in $n$-dimensional Euclidean space bounded by hyperplanes), thus solving problems posed by Grabiner [J. Combin. Theory Ser. A 97 (2002), 285-306]. These results include asymptotic expressions for the number of vicious walkers on a circle, and as well for the number of vicious walkers in an interval. The proofs depart from the exact results of Grabiner [loc. cit.], and require as diverse means as results from symmetric function theory and the saddle point method, among others.

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