Geodesic
Asymptotics for Random Walks in Alcoves of Affine Weyl Groups
Séminaire lotharingien de combinatoire, Tome 52 (2004-2007)

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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. 

@article{SLC_2004-2007_52_a8,
     author = {Christian Krattenthaler},
     title = {Asymptotics for {Random} {Walks} in {Alcoves} of {Affine} {Weyl} {Groups}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {52},
     year = {2004-2007},
     url = {http://geodesic.mathdoc.fr/item/SLC_2004-2007_52_a8/}
}
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Christian Krattenthaler. Asymptotics for Random Walks in Alcoves of Affine Weyl Groups. Séminaire lotharingien de combinatoire, Tome 52 (2004-2007). http://geodesic.mathdoc.fr/item/SLC_2004-2007_52_a8/