Christian Krattenthaler
Published 2003-01-19, updated 2008-01-11Version 3
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.
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
Journal: S\'eminaire Lotharingien Combin. 52 (2007), Article B52i, 72 pp
Asymptotics for the Number of Random Walks in the Euclidean Lattice
A product formula for multivariate Rogers-Szegö polynomials
Poincare series of subsets of affine Weyl groups
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