Asymptotics for the number of walks in a Weyl chamber of type B

Abstract. We consider lattice walks in R confined to the region 0 < x1 < x2... < xk with fixed (but arbitrary) starting and end points. The walks are required to be ”reflectable”, that is, we assume that the number of paths can be counted using the reflection principle. The main result is an asymptotic formula for the total number of walks of length n for a general class of walks as n tends to infinity. As applications, we find the asymptotics for the number of k-non-crossing tangled diagrams on the set {1, 2, ..., n} as n tends to infinity, the asymptotics for the number of k-vicious walkers subject to a wall restriction in the random turns model, and we re-derive known asymptotics for the number of k-vicious walkers subject to a wall restriction in the lock step model.