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 <alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pghv4p042p" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" />ℝk</alternatives> confined to the region <alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pghv4p0415" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" />0<x1<x2…<xk</alternatives> 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