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Keywords:

  • lattice walks;
  • Weyl chamber;
  • asymptotics;
  • determinants;
  • saddle point method

ABSTRACT

We consider lattice walks in inline image confined to the region inline image 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