Asymptotics for the number of walks in a Weyl chamber of type B
We consider lattice walks in confined to the region with fixed (but arbitrary) starting and end points. These walks are assumed to be such that their number can be counted using a reflection principle argument. The main results are asymptotic formulas for the total number of walks of length n with either a fixed or a free end point 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 as well as asymptotics for two k-vicious walkers models subject to a wall restriction.  2012 Wiley Periodicals, Inc. Random Struct. Alg., 45, 261305, 2014
asymptotics weyl chamber lattice walks determinants saddle point method