Séminaire Lotharingien de Combinatoire, B52i (2007), 72 pp.

Christian Krattenthaler

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 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, as well as 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.

Received: December 11, 2006. Accepted: April 26, 2007. Final Version: December 31, 2007.

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