Asymptotics for the number of walks in a Weyl chamber of type B. Issue 2 (8th October 2012) - Feierl, Thomas
ABSTRACT We consider lattice walks in ℝk confined to the region 0<x1<x2…<xk 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, 261–305, 2014