Séminaire Lotharingien de Combinatoire, B52i (2007), 72 pp.
Asymptotics for Random Walks in Alcoves of Affine Weyl Groups
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,
Received: December 11, 2006.
Accepted: April 26, 2007.
Final Version: December 31, 2007.
The following versions are available: