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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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