Asymptotics for random walks in alcoves of affine Weyl groups
Abstract
Asymptotic results are derived for the number of random walks in alcoves of affine Weyl groups (which are certain regions in -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.
Cite
@article{arxiv.math/0301203,
title = {Asymptotics for random walks in alcoves of affine Weyl groups},
author = {Christian Krattenthaler},
journal= {arXiv preprint arXiv:math/0301203},
year = {2011}
}
Comments
72 pages, AmS-LaTeX; major revision: there are now also theorems on the asymptotic enumeration with non-fixed end points in types B and D; a flaw in the statement and proof of Lemma A has been corrected