## Christian Krattenthaler

# Asymptotics for random walks in alcoves of affine Weyl groups

### (72 pages)

**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.
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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